28x^2+28x-96=0

Solution for 28x^2+28x-96=0 equation:

Simplifying
28x2 + 28x + -96 = 0

Reorder the terms:
-96 + 28x + 28x2 = 0

Solving
-96 + 28x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-24 + 7x + 7x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-24 + 7x + 7x2)' equal to zero and attempt to solve:

Simplifying
-24 + 7x + 7x2 = 0

Solving
-24 + 7x + 7x2 = 0

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

Divide each side by '7'.
-3.428571429 + x + x2 = 0

Move the constant term to the right:

Add '3.428571429' to each side of the equation.
-3.428571429 + x + 3.428571429 + x2 = 0 + 3.428571429

Reorder the terms:
-3.428571429 + 3.428571429 + x + x2 = 0 + 3.428571429

Combine like terms: -3.428571429 + 3.428571429 = 0.000000000
0.000000000 + x + x2 = 0 + 3.428571429
x + x2 = 0 + 3.428571429

Combine like terms: 0 + 3.428571429 = 3.428571429
x + x2 = 3.428571429

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 3.428571429 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 3.428571429 + 0.25

Combine like terms: 3.428571429 + 0.25 = 3.678571429
1.25 + x2 = 3.678571429

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 3.678571429

Calculate the square root of the right side: 1.917960226

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.917960226 and -1.917960226.

Subproblem 1
x + 0.5 = 1.917960226

Simplifying
x + 0.5 = 1.917960226

Reorder the terms:
0.5 + x = 1.917960226

Solving
0.5 + x = 1.917960226

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.917960226 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.917960226 + -0.5
x = 1.917960226 + -0.5

Combine like terms: 1.917960226 + -0.5 = 1.417960226
x = 1.417960226

Simplifying
x = 1.417960226

Subproblem 2
x + 0.5 = -1.917960226

Simplifying
x + 0.5 = -1.917960226

Reorder the terms:
0.5 + x = -1.917960226

Solving
0.5 + x = -1.917960226

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.917960226 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.917960226 + -0.5
x = -1.917960226 + -0.5

Combine like terms: -1.917960226 + -0.5 = -2.417960226
x = -2.417960226

Simplifying
x = -2.417960226

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.417960226, -2.417960226}
Solution
x = {1.417960226, -2.417960226}