6b^2-6b=12

Solution for 6b^2-6b=12 equation:

Simplifying
6b2 + -6b = 12

Reorder the terms:
-6b + 6b2 = 12

Solving
-6b + 6b2 = 12

Solving for variable 'b'.

Reorder the terms:
-12 + -6b + 6b2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -6b + 6b2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + -1b + b2) = 0

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

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

Simplifying
-1 + -1b = 0

Solving
-1 + -1b = 0

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

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

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

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

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

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

Simplifying
2 + -1b = 0

Solving
2 + -1b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1b = 0 + -2

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

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

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

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