12x=-10-2x^2

Solution for 12x=-10-2x^2 equation:

Simplifying
12x = -10 + -2x2

Solving
12x = -10 + -2x2

Solving for variable 'x'.

Reorder the terms:
10 + 12x + 2x2 = -10 + -2x2 + 10 + 2x2

Reorder the terms:
10 + 12x + 2x2 = -10 + 10 + -2x2 + 2x2

Combine like terms: -10 + 10 = 0
10 + 12x + 2x2 = 0 + -2x2 + 2x2
10 + 12x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
10 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 6x + x2) = 0

Factor a trinomial.
2((5 + x)(1 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -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 = {-5, -1}