x^2+7x-6=9x-6

Solution for x^2+7x-6=9x-6 equation:

Simplifying
x2 + 7x + -6 = 9x + -6

Reorder the terms:
-6 + 7x + x2 = 9x + -6

Reorder the terms:
-6 + 7x + x2 = -6 + 9x

Add '6' to each side of the equation.
-6 + 7x + 6 + x2 = -6 + 6 + 9x

Reorder the terms:
-6 + 6 + 7x + x2 = -6 + 6 + 9x

Combine like terms: -6 + 6 = 0
0 + 7x + x2 = -6 + 6 + 9x
7x + x2 = -6 + 6 + 9x

Combine like terms: -6 + 6 = 0
7x + x2 = 0 + 9x
7x + x2 = 9x

Solving
7x + x2 = 9x

Solving for variable 'x'.

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

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

Combine like terms: 9x + -9x = 0
-2x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2 + x) = 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 '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

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

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

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

Simplifying
x = 2
Solution
x = {0, 2}