6X^2+66X=-180

Solution for 6X^2+66X=-180 equation:

Simplifying
6X2 + 66X = -180

Reorder the terms:
66X + 6X2 = -180

Solving
66X + 6X2 = -180

Solving for variable 'X'.

Reorder the terms:
180 + 66X + 6X2 = -180 + 180

Combine like terms: -180 + 180 = 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}