6(x^2-x)=12

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

Simplifying
6(x2 + -1x) = 12

Reorder the terms:
6(-1x + x2) = 12
(-1x * 6 + x2 * 6) = 12
(-6x + 6x2) = 12

Solving
-6x + 6x2 = 12

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + -1x + x2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1, 2}