(3x^2-108)-(4x^2+24x)=

Solution for (3x^2-108)-(4x^2+24x)= equation:

Simplifying
(3x2 + -108) + -1(4x2 + 24x) = 0

Reorder the terms:
(-108 + 3x2) + -1(4x2 + 24x) = 0

Remove parenthesis around (-108 + 3x2)
-108 + 3x2 + -1(4x2 + 24x) = 0

Reorder the terms:
-108 + 3x2 + -1(24x + 4x2) = 0
-108 + 3x2 + (24x * -1 + 4x2 * -1) = 0
-108 + 3x2 + (-24x + -4x2) = 0

Reorder the terms:
-108 + -24x + 3x2 + -4x2 = 0

Combine like terms: 3x2 + -4x2 = -1x2
-108 + -24x + -1x2 = 0

Solving
-108 + -24x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(108 + 24x + x2) = 0

Factor a trinomial.
-1((18 + x)(6 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(18 + x)' equal to zero and attempt to solve:

Simplifying
18 + x = 0

Solving
18 + x = 0

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

Add '-18' to each side of the equation.
18 + -18 + x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + x = 0 + -18
x = 0 + -18

Combine like terms: 0 + -18 = -18
x = -18

Simplifying
x = -18
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 = {-18, -6}