9x^2-10x=7x^2+15x

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Solution for 9x^2-10x=7x^2+15x equation: 


Simplifying
9x2 + -10x = 7x2 + 15x

Reorder the terms:
-10x + 9x2 = 7x2 + 15x

Reorder the terms:
-10x + 9x2 = 15x + 7x2

Solving
-10x + 9x2 = 15x + 7x2

Solving for variable 'x'.

Reorder the terms:
-10x + -15x + 9x2 + -7x2 = 15x + 7x2 + -15x + -7x2

Combine like terms: -10x + -15x = -25x
-25x + 9x2 + -7x2 = 15x + 7x2 + -15x + -7x2

Combine like terms: 9x2 + -7x2 = 2x2
-25x + 2x2 = 15x + 7x2 + -15x + -7x2

Reorder the terms:
-25x + 2x2 = 15x + -15x + 7x2 + -7x2

Combine like terms: 15x + -15x = 0
-25x + 2x2 = 0 + 7x2 + -7x2
-25x + 2x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-25x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-25 + 2x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(-25 + 2x)' equal to zero and attempt to solve:

Simplifying
-25 + 2x = 0

Solving
-25 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '25' to each side of the equation.
-25 + 25 + 2x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 2x = 0 + 25
2x = 0 + 25

Combine like terms: 0 + 25 = 25
2x = 25

Divide each side by '2'.
x = 12.5

Simplifying
x = 12.5
Solution
x = {0, 12.5}

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