0=12x^2+6x-6

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

Simplifying
0 = 12x2 + 6x + -6

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

Solving
0 = -6 + 6x + 12x2

Solving for variable 'x'.

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

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

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

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

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

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

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

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

Simplifying
1 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
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 = {0.5, -1}