x^2-6=6x-6

Solution for x^2-6=6x-6 equation:

Simplifying
x2 + -6 = 6x + -6

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

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

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

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

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

Solving
x2 = 6x

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + 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 '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
Solution
x = {0, 6}