3x*(x+15)=-108

Solution for 3x*(x+15)=-108 equation:

Simplifying
3x(x + 15) = -108

Reorder the terms:
3x(15 + x) = -108
(15 * 3x + x * 3x) = -108
(45x + 3x2) = -108

Solving
45x + 3x2 = -108

Solving for variable 'x'.

Reorder the terms:
108 + 45x + 3x2 = -108 + 108

Combine like terms: -108 + 108 = 0
108 + 45x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(36 + 15x + x2) = 0

Factor a trinomial.
3((12 + x)(3 + 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 '(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 = {-12, -3}