12x^2=-18x-6

Solution for 12x^2=-18x-6 equation:

Simplifying
12x2 = -18x + -6

Reorder the terms:
12x2 = -6 + -18x

Solving
12x2 = -6 + -18x

Solving for variable 'x'.

Reorder the terms:
6 + 18x + 12x2 = -6 + -18x + 6 + 18x

Reorder the terms:
6 + 18x + 12x2 = -6 + 6 + -18x + 18x

Combine like terms: -6 + 6 = 0
6 + 18x + 12x2 = 0 + -18x + 18x
6 + 18x + 12x2 = -18x + 18x

Combine like terms: -18x + 18x = 0
6 + 18x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 3x + 2x2) = 0

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

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
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
Solution
x = {-1, -0.5}