3x^2+54x=-216

Solution for 3x^2+54x=-216 equation:

Simplifying
3x2 + 54x = -216

Reorder the terms:
54x + 3x2 = -216

Solving
54x + 3x2 = -216

Solving for variable 'x'.

Reorder the terms:
216 + 54x + 3x2 = -216 + 216

Combine like terms: -216 + 216 = 0
216 + 54x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(72 + 18x + x2) = 0

Factor a trinomial.
3((12 + x)(6 + x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
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 = {-12, -6}