10x^2+120x-960=0

Solution for 10x^2+120x-960=0 equation:

Simplifying
10x2 + 120x + -960 = 0

Reorder the terms:
-960 + 120x + 10x2 = 0

Solving
-960 + 120x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-96 + 12x + x2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-96 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
-96 + 12x + x2 = 0

Solving
-96 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + 12x + 96 + x2 = 0 + 96

Reorder the terms:
-96 + 96 + 12x + x2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + 12x + x2 = 0 + 96
12x + x2 = 0 + 96

Combine like terms: 0 + 96 = 96
12x + x2 = 96

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 96 + 36

Reorder the terms:
36 + 12x + x2 = 96 + 36

Combine like terms: 96 + 36 = 132
36 + 12x + x2 = 132

Factor a perfect square on the left side:
(x + 6)(x + 6) = 132

Calculate the square root of the right side: 11.489125293

Break this problem into two subproblems by setting 
(x + 6) equal to 11.489125293 and -11.489125293.

Subproblem 1
x + 6 = 11.489125293

Simplifying
x + 6 = 11.489125293

Reorder the terms:
6 + x = 11.489125293

Solving
6 + x = 11.489125293

Solving for variable 'x'.

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 = 11.489125293 + -6

Combine like terms: 6 + -6 = 0
0 + x = 11.489125293 + -6
x = 11.489125293 + -6

Combine like terms: 11.489125293 + -6 = 5.489125293
x = 5.489125293

Simplifying
x = 5.489125293

Subproblem 2
x + 6 = -11.489125293

Simplifying
x + 6 = -11.489125293

Reorder the terms:
6 + x = -11.489125293

Solving
6 + x = -11.489125293

Solving for variable 'x'.

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 = -11.489125293 + -6

Combine like terms: 6 + -6 = 0
0 + x = -11.489125293 + -6
x = -11.489125293 + -6

Combine like terms: -11.489125293 + -6 = -17.489125293
x = -17.489125293

Simplifying
x = -17.489125293

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.489125293, -17.489125293}
Solution
x = {5.489125293, -17.489125293}