# Solve Math Equations

Math equation solver is a site which can help you to solve any math problem.We help you to generate  solutions to specific math questions which you have entered. The main advantage is tha solution will be step by step.  We are available 24 x 7.This will help you to understand the problem in a better way and also help you to master the procedure of solving math equations.
When two mathematical expressions are equated with an "=" sign, we get a math equation. One or both sides of the equation may contain variables. By solving a math equation, we are trying to find a single value which satisfies the math equation. That is when we substitute the value of the solution for the variable, the equation balances.

## Steps to solve math equation

There is no hard and fast rule to solve all equations. But our ultimate aim in solving math equations will be to find a single value for the variables involved in the problem. There are different types of equations.Following are few of them.
• Linear equation
• Equation containing radicals
• Equations containing absolute values
• Equations containing fractions
• Exponential equation
• Logarithmic equation
There are many other types of equation also.  You may enter any of these types of equations. You will get step by step solution to all your questions.

## Solve any Math Equation

Following are simple sample solutions of the math equations.

Example 1: -

Solve the equation 5x - 4 = 2x - 6

Solution: -

Given equation is 5x - 4 = 2x - 6
Here there is only one variable involved in the problem.  So to solve, we just have to isolate the variable. For this we take all variables to one side and all constants to other.
Lets first take the constants to the right side of the equation.  For this, we add 4 on both sides, we get
5x = 2x -2
Now we take the variables on the left side of the equation.  For this, we subtract 2x on both sides, we get
3x = 2
Now we have variable on the left side and constant on the right side of the equation
Dividing by 3 on both sides, we get the required solution
x = 2/3
Solution: x = 2/3

Example 2: -

Solve the equation (x - 1)(x - 3 )(x - 5)(x - 7) = 9

Solution: -

Given equation is (x - 1)(x - 3 )(x - 5)(x - 7) = 9
Here there is only one variable involved in the problem.  So to solve, we just have to isolate the variable. First we rearrange the factors.
So the equation becomes
(x - 1)(x - 7 )(x - 3)(x - 5) = 9
Now we combine the terms, we get
(x2 - 8x + 7)(x2 - 8x +15) = 9

Step 1:

Take x2 - 8x as u. Then the equation becomes (u + 7)(u + 15) = 9
Simplifying the left side we get
u2 + 7u + 15u + 105 = 9
That is
u2 + 22u + 105 = 9
subtracting 9 on both sides, we get
u2 + 22u + 96 = 0
Now we split the middle term
u2 + 16u + 6u + 96 = 0
Taking u common from first two terms and 6 common from last two terms, we get
u (u + 16) + 6 (u + 16) = 0
Now we take u + 16 common, we get
(u + 16) ( u + 6) = 0
Equating each factor to 0, we get
u + 16 = 0 ⇒ u = -16
and u + 6 = 0 ⇒ u = -6

Step 2:
When u = -16
x2 - 8x =  -16
Adding 16 on both sides, we get
x2 - 8x + 16 = 0
Now we split the middle term
x2 - 4x - 4x + 16 = 0
Taking x common from first two terms and -4 common from last two terms, we get
x (x - 4) - 4 (x - 4) = 0
Now we take x - 4 common, we get
(x - 4) ( x - 4) = 0
Equating each factor to 0, we get
x - 4 = 0 ⇒ x = 4
and x - 4 = 0 ⇒ x = 4

Step 3:
When u = -6
x2 - 8x =  -6
Adding 6 on both sides, we get
x2 - 8x + 6 = 0
We use the quadratic formula to solve this equation.
x = [-(-8) ±√((-8)2 - 4 x 1 x 6)] / 2
= (8 ±√40)/2
= 4 ±√10
Therefore solutions are 4, 4, 4±√10

Example 3: -

Solve the equation log(x - 9) + log x = 1

Solution: -

Given equation is log(x - 9) + log x = 1
Here there is only one variable involved in the problem.  So to solve, we just have to isolate the variable.First we have to get rid of the log
We know that log a + log b = log ab
So the left side becomes
log (x - 9)x = 1
Also we know that ax = b ⇒ loga b = x
So we can write the above equation as
(x - 9)x = 101
That is x2 - 9x = 10.
This is quadratic equation.  Lets solve it by grouping.
Subtracting 10 on both sides, we get
x2 - 9x - 10 = 0
Now we split the middle term
x2 - 10x + x -10 = 0
Taking x common from first two terms and 1 common from last two terms, we get
x (x - 10) + 1 (x - 10) = 0
Now we take x - 10 common, we get
(x - 10) ( x + 1) = 0
Equating each factor to 0, we get
x - 10 = 0 ⇒ x = 10
and x + 1 = 0 ⇒ x = -1
When we substitute these values of x in the equation, we can see that -1 is not a solution
Therefore solution is : x = 10