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

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

Simplifying
-54x2 + -24x + -2 = 0

Reorder the terms:
-2 + -24x + -54x2 = 0

Solving
-2 + -24x + -54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(1 + 12x + 27x2) = 0

Factor a trinomial.
-2((1 + 3x)(1 + 9x)) = 0

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

Simplifying
1 + 3x = 0

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

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

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

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Subproblem 2
Set the factor '(1 + 9x)' equal to zero and attempt to solve:

Simplifying
1 + 9x = 0

Solving
1 + 9x = 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 + 9x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9x = 0 + -1
9x = 0 + -1

Combine like terms: 0 + -1 = -1
9x = -1

Divide each side by '9'.
x = -0.1111111111

Simplifying
x = -0.1111111111
Solution
x = {-0.3333333333, -0.1111111111}