-12x-71=3x^2+24x+37

Solution for -12x-71=3x^2+24x+37 equation:

Simplifying
-12x + -71 = 3x2 + 24x + 37

Reorder the terms:
-71 + -12x = 3x2 + 24x + 37

Reorder the terms:
-71 + -12x = 37 + 24x + 3x2

Solving
-71 + -12x = 37 + 24x + 3x2

Solving for variable 'x'.

Reorder the terms:
-71 + -37 + -12x + -24x + -3x2 = 37 + 24x + 3x2 + -37 + -24x + -3x2

Combine like terms: -71 + -37 = -108
-108 + -12x + -24x + -3x2 = 37 + 24x + 3x2 + -37 + -24x + -3x2

Combine like terms: -12x + -24x = -36x
-108 + -36x + -3x2 = 37 + 24x + 3x2 + -37 + -24x + -3x2

Reorder the terms:
-108 + -36x + -3x2 = 37 + -37 + 24x + -24x + 3x2 + -3x2

Combine like terms: 37 + -37 = 0
-108 + -36x + -3x2 = 0 + 24x + -24x + 3x2 + -3x2
-108 + -36x + -3x2 = 24x + -24x + 3x2 + -3x2

Combine like terms: 24x + -24x = 0
-108 + -36x + -3x2 = 0 + 3x2 + -3x2
-108 + -36x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-108 + -36x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(36 + 12x + x2) = 0

Factor a trinomial.
-3((6 + x)(6 + x)) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

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

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

Simplifying
x = -6
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

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

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

Simplifying
x = -6
Solution
x = {-6, -6}