2x-12=6x(x-6)

Solution for 2x-12=6x(x-6) equation:

Simplifying
2x + -12 = 6x(x + -6)

Reorder the terms:
-12 + 2x = 6x(x + -6)

Reorder the terms:
-12 + 2x = 6x(-6 + x)
-12 + 2x = (-6 * 6x + x * 6x)
-12 + 2x = (-36x + 6x2)

Solving
-12 + 2x = -36x + 6x2

Solving for variable 'x'.

Combine like terms: 2x + 36x = 38x
-12 + 38x + -6x2 = -36x + 6x2 + 36x + -6x2

Reorder the terms:
-12 + 38x + -6x2 = -36x + 36x + 6x2 + -6x2

Combine like terms: -36x + 36x = 0
-12 + 38x + -6x2 = 0 + 6x2 + -6x2
-12 + 38x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-12 + 38x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 19x + -3x2) = 0

Factor a trinomial.
2((-6 + x)(1 + -3x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {6, 0.3333333333}