6x^2=-36x-54

Solution for 6x^2=-36x-54 equation:

Simplifying
6x2 = -36x + -54

Reorder the terms:
6x2 = -54 + -36x

Solving
6x2 = -54 + -36x

Solving for variable 'x'.

Reorder the terms:
54 + 36x + 6x2 = -54 + -36x + 54 + 36x

Reorder the terms:
54 + 36x + 6x2 = -54 + 54 + -36x + 36x

Combine like terms: -54 + 54 = 0
54 + 36x + 6x2 = 0 + -36x + 36x
54 + 36x + 6x2 = -36x + 36x

Combine like terms: -36x + 36x = 0
54 + 36x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(9 + 6x + x2) = 0

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

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

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {-3, -3}