108x^2-6x-30=0

Solution for 108x^2-6x-30=0 equation:

Simplifying
108x2 + -6x + -30 = 0

Reorder the terms:
-30 + -6x + 108x2 = 0

Solving
-30 + -6x + 108x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-5 + -1x + 18x2) = 0

Factor a trinomial.
6((-1 + -2x)(5 + -9x)) = 0

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(5 + -9x)' equal to zero and attempt to solve:

Simplifying
5 + -9x = 0

Solving
5 + -9x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -9x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9x = 0 + -5
-9x = 0 + -5

Combine like terms: 0 + -5 = -5
-9x = -5

Divide each side by '-9'.
x = 0.5555555556

Simplifying
x = 0.5555555556
Solution
x = {-0.5, 0.5555555556}