0=108x^2-120x-96

Solution for 0=108x^2-120x-96 equation:

Simplifying
0 = 108x2 + -120x + -96

Reorder the terms:
0 = -96 + -120x + 108x2

Solving
0 = -96 + -120x + 108x2

Solving for variable 'x'.

Combine like terms: 0 + 96 = 96
96 + 120x + -108x2 = -96 + -120x + 108x2 + 96 + 120x + -108x2

Reorder the terms:
96 + 120x + -108x2 = -96 + 96 + -120x + 120x + 108x2 + -108x2

Combine like terms: -96 + 96 = 0
96 + 120x + -108x2 = 0 + -120x + 120x + 108x2 + -108x2
96 + 120x + -108x2 = -120x + 120x + 108x2 + -108x2

Combine like terms: -120x + 120x = 0
96 + 120x + -108x2 = 0 + 108x2 + -108x2
96 + 120x + -108x2 = 108x2 + -108x2

Combine like terms: 108x2 + -108x2 = 0
96 + 120x + -108x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(8 + 10x + -9x2) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(8 + 10x + -9x2)' equal to zero and attempt to solve:

Simplifying
8 + 10x + -9x2 = 0

Solving
8 + 10x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-0.8888888889 + -1.111111111x + x2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + -1.111111111x + 0.8888888889 + x2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + -1.111111111x + x2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + -1.111111111x + x2 = 0 + 0.8888888889
-1.111111111x + x2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
-1.111111111x + x2 = 0.8888888889

The x term is -1.111111111x.  Take half its coefficient (-0.5555555555).
Square it (0.3086419752) and add it to both sides.

Add '0.3086419752' to each side of the equation.
-1.111111111x + 0.3086419752 + x2 = 0.8888888889 + 0.3086419752

Reorder the terms:
0.3086419752 + -1.111111111x + x2 = 0.8888888889 + 0.3086419752

Combine like terms: 0.8888888889 + 0.3086419752 = 1.1975308641
0.3086419752 + -1.111111111x + x2 = 1.1975308641

Factor a perfect square on the left side:
(x + -0.5555555555)(x + -0.5555555555) = 1.1975308641

Calculate the square root of the right side: 1.094317533

Break this problem into two subproblems by setting 
(x + -0.5555555555) equal to 1.094317533 and -1.094317533.

Subproblem 1
x + -0.5555555555 = 1.094317533

Simplifying
x + -0.5555555555 = 1.094317533

Reorder the terms:
-0.5555555555 + x = 1.094317533

Solving
-0.5555555555 + x = 1.094317533

Solving for variable 'x'.

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

Add '0.5555555555' to each side of the equation.
-0.5555555555 + 0.5555555555 + x = 1.094317533 + 0.5555555555

Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000
0.0000000000 + x = 1.094317533 + 0.5555555555
x = 1.094317533 + 0.5555555555

Combine like terms: 1.094317533 + 0.5555555555 = 1.6498730885
x = 1.6498730885

Simplifying
x = 1.6498730885

Subproblem 2
x + -0.5555555555 = -1.094317533

Simplifying
x + -0.5555555555 = -1.094317533

Reorder the terms:
-0.5555555555 + x = -1.094317533

Solving
-0.5555555555 + x = -1.094317533

Solving for variable 'x'.

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

Add '0.5555555555' to each side of the equation.
-0.5555555555 + 0.5555555555 + x = -1.094317533 + 0.5555555555

Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000
0.0000000000 + x = -1.094317533 + 0.5555555555
x = -1.094317533 + 0.5555555555

Combine like terms: -1.094317533 + 0.5555555555 = -0.5387619775
x = -0.5387619775

Simplifying
x = -0.5387619775

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.6498730885, -0.5387619775}
Solution
x = {1.6498730885, -0.5387619775}