-2x(2x+7)-7(-8x-6)=-76

Solution for -2x(2x+7)-7(-8x-6)=-76 equation:

Simplifying
-2x(2x + 7) + -7(-8x + -6) = -76

Reorder the terms:
-2x(7 + 2x) + -7(-8x + -6) = -76
(7 * -2x + 2x * -2x) + -7(-8x + -6) = -76
(-14x + -4x2) + -7(-8x + -6) = -76

Reorder the terms:
-14x + -4x2 + -7(-6 + -8x) = -76
-14x + -4x2 + (-6 * -7 + -8x * -7) = -76
-14x + -4x2 + (42 + 56x) = -76

Reorder the terms:
42 + -14x + 56x + -4x2 = -76

Combine like terms: -14x + 56x = 42x
42 + 42x + -4x2 = -76

Solving
42 + 42x + -4x2 = -76

Solving for variable 'x'.

Reorder the terms:
42 + 76 + 42x + -4x2 = -76 + 76

Combine like terms: 42 + 76 = 118
118 + 42x + -4x2 = -76 + 76

Combine like terms: -76 + 76 = 0
118 + 42x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(59 + 21x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(59 + 21x + -2x2)' equal to zero and attempt to solve:

Simplifying
59 + 21x + -2x2 = 0

Solving
59 + 21x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-29.5 + -10.5x + x2 = 0

Move the constant term to the right:

Add '29.5' to each side of the equation.
-29.5 + -10.5x + 29.5 + x2 = 0 + 29.5

Reorder the terms:
-29.5 + 29.5 + -10.5x + x2 = 0 + 29.5

Combine like terms: -29.5 + 29.5 = 0.0
0.0 + -10.5x + x2 = 0 + 29.5
-10.5x + x2 = 0 + 29.5

Combine like terms: 0 + 29.5 = 29.5
-10.5x + x2 = 29.5

The x term is -10.5x.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5x + 27.5625 + x2 = 29.5 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = 29.5 + 27.5625

Combine like terms: 29.5 + 27.5625 = 57.0625
27.5625 + -10.5x + x2 = 57.0625

Factor a perfect square on the left side:
(x + -5.25)(x + -5.25) = 57.0625

Calculate the square root of the right side: 7.553972465

Break this problem into two subproblems by setting 
(x + -5.25) equal to 7.553972465 and -7.553972465.

Subproblem 1
x + -5.25 = 7.553972465

Simplifying
x + -5.25 = 7.553972465

Reorder the terms:
-5.25 + x = 7.553972465

Solving
-5.25 + x = 7.553972465

Solving for variable 'x'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + x = 7.553972465 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + x = 7.553972465 + 5.25
x = 7.553972465 + 5.25

Combine like terms: 7.553972465 + 5.25 = 12.803972465
x = 12.803972465

Simplifying
x = 12.803972465

Subproblem 2
x + -5.25 = -7.553972465

Simplifying
x + -5.25 = -7.553972465

Reorder the terms:
-5.25 + x = -7.553972465

Solving
-5.25 + x = -7.553972465

Solving for variable 'x'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + x = -7.553972465 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + x = -7.553972465 + 5.25
x = -7.553972465 + 5.25

Combine like terms: -7.553972465 + 5.25 = -2.303972465
x = -2.303972465

Simplifying
x = -2.303972465

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.803972465, -2.303972465}
Solution
x = {12.803972465, -2.303972465}