12x^2+87x+102=-6-3x

Solution for 12x^2+87x+102=-6-3x equation:

Simplifying
12x2 + 87x + 102 = -6 + -3x

Reorder the terms:
102 + 87x + 12x2 = -6 + -3x

Solving
102 + 87x + 12x2 = -6 + -3x

Solving for variable 'x'.

Reorder the terms:
102 + 6 + 87x + 3x + 12x2 = -6 + -3x + 6 + 3x

Combine like terms: 102 + 6 = 108
108 + 87x + 3x + 12x2 = -6 + -3x + 6 + 3x

Combine like terms: 87x + 3x = 90x
108 + 90x + 12x2 = -6 + -3x + 6 + 3x

Reorder the terms:
108 + 90x + 12x2 = -6 + 6 + -3x + 3x

Combine like terms: -6 + 6 = 0
108 + 90x + 12x2 = 0 + -3x + 3x
108 + 90x + 12x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
108 + 90x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(18 + 15x + 2x2) = 0

Factor a trinomial.
6((6 + x)(3 + 2x)) = 0

Ignore the factor 6.
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 '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {-6, -1.5}