(-6x^2)+6x+12=0

Solution for (-6x^2)+6x+12=0 equation:

Simplifying
(-6x2) + 6x + 12 = 0

Reorder the terms:
12 + 6x + (-6x2) = 0

Solving
12 + 6x + (-6x2) = 0

Solving for variable 'x'.

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

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

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

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