-24x^2-54x-12=0

Solution for -24x^2-54x-12=0 equation:

Simplifying
-24x2 + -54x + -12 = 0

Reorder the terms:
-12 + -54x + -24x2 = 0

Solving
-12 + -54x + -24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-6'.
-6(2 + 9x + 4x2) = 0

Factor a trinomial.
-6((2 + x)(1 + 4x)) = 0

Ignore the factor -6.
Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {-2, -0.25}