3x^2+27x=108

Solution for 3x^2+27x=108 equation:

Simplifying
3x2 + 27x = 108

Reorder the terms:
27x + 3x2 = 108

Solving
27x + 3x2 = 108

Solving for variable 'x'.

Reorder the terms:
-108 + 27x + 3x2 = 108 + -108

Combine like terms: 108 + -108 = 0
-108 + 27x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-36 + 9x + x2) = 0

Factor a trinomial.
3((-12 + -1x)(3 + -1x)) = 0

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

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 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 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-12, 3}