6x^2+66x+178=-2

Solution for 6x^2+66x+178=-2 equation:

Simplifying
6x2 + 66x + 178 = -2

Reorder the terms:
178 + 66x + 6x2 = -2

Solving
178 + 66x + 6x2 = -2

Solving for variable 'x'.

Reorder the terms:
178 + 2 + 66x + 6x2 = -2 + 2

Combine like terms: 178 + 2 = 180
180 + 66x + 6x2 = -2 + 2

Combine like terms: -2 + 2 = 0
180 + 66x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(30 + 11x + x2) = 0

Factor a trinomial.
6((6 + x)(5 + x)) = 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 '(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
Solution
x = {-6, -5}