-527=-8x(-5+12x)-7

Solution for -527=-8x(-5+12x)-7 equation:

Simplifying
-527 = -8x(-5 + 12x) + -7
-527 = (-5 * -8x + 12x * -8x) + -7
-527 = (40x + -96x2) + -7

Reorder the terms:
-527 = -7 + 40x + -96x2

Solving
-527 = -7 + 40x + -96x2

Solving for variable 'x'.

Combine like terms: -527 + 7 = -520
-520 + -40x + 96x2 = -7 + 40x + -96x2 + 7 + -40x + 96x2

Reorder the terms:
-520 + -40x + 96x2 = -7 + 7 + 40x + -40x + -96x2 + 96x2

Combine like terms: -7 + 7 = 0
-520 + -40x + 96x2 = 0 + 40x + -40x + -96x2 + 96x2
-520 + -40x + 96x2 = 40x + -40x + -96x2 + 96x2

Combine like terms: 40x + -40x = 0
-520 + -40x + 96x2 = 0 + -96x2 + 96x2
-520 + -40x + 96x2 = -96x2 + 96x2

Combine like terms: -96x2 + 96x2 = 0
-520 + -40x + 96x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-65 + -5x + 12x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-65 + -5x + 12x2)' equal to zero and attempt to solve:

Simplifying
-65 + -5x + 12x2 = 0

Solving
-65 + -5x + 12x2 = 0

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

Divide each side by '12'.
-5.416666667 + -0.4166666667x + x2 = 0

Move the constant term to the right:

Add '5.416666667' to each side of the equation.
-5.416666667 + -0.4166666667x + 5.416666667 + x2 = 0 + 5.416666667

Reorder the terms:
-5.416666667 + 5.416666667 + -0.4166666667x + x2 = 0 + 5.416666667

Combine like terms: -5.416666667 + 5.416666667 = 0.000000000
0.000000000 + -0.4166666667x + x2 = 0 + 5.416666667
-0.4166666667x + x2 = 0 + 5.416666667

Combine like terms: 0 + 5.416666667 = 5.416666667
-0.4166666667x + x2 = 5.416666667

The x term is -0.4166666667x.  Take half its coefficient (-0.2083333334).
Square it (0.04340277781) and add it to both sides.

Add '0.04340277781' to each side of the equation.
-0.4166666667x + 0.04340277781 + x2 = 5.416666667 + 0.04340277781

Reorder the terms:
0.04340277781 + -0.4166666667x + x2 = 5.416666667 + 0.04340277781

Combine like terms: 5.416666667 + 0.04340277781 = 5.46006944481
0.04340277781 + -0.4166666667x + x2 = 5.46006944481

Factor a perfect square on the left side:
(x + -0.2083333334)(x + -0.2083333334) = 5.46006944481

Calculate the square root of the right side: 2.336679149

Break this problem into two subproblems by setting 
(x + -0.2083333334) equal to 2.336679149 and -2.336679149.

Subproblem 1
x + -0.2083333334 = 2.336679149

Simplifying
x + -0.2083333334 = 2.336679149

Reorder the terms:
-0.2083333334 + x = 2.336679149

Solving
-0.2083333334 + x = 2.336679149

Solving for variable 'x'.

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

Add '0.2083333334' to each side of the equation.
-0.2083333334 + 0.2083333334 + x = 2.336679149 + 0.2083333334

Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000
0.0000000000 + x = 2.336679149 + 0.2083333334
x = 2.336679149 + 0.2083333334

Combine like terms: 2.336679149 + 0.2083333334 = 2.5450124824
x = 2.5450124824

Simplifying
x = 2.5450124824

Subproblem 2
x + -0.2083333334 = -2.336679149

Simplifying
x + -0.2083333334 = -2.336679149

Reorder the terms:
-0.2083333334 + x = -2.336679149

Solving
-0.2083333334 + x = -2.336679149

Solving for variable 'x'.

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

Add '0.2083333334' to each side of the equation.
-0.2083333334 + 0.2083333334 + x = -2.336679149 + 0.2083333334

Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000
0.0000000000 + x = -2.336679149 + 0.2083333334
x = -2.336679149 + 0.2083333334

Combine like terms: -2.336679149 + 0.2083333334 = -2.1283458156
x = -2.1283458156

Simplifying
x = -2.1283458156

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.5450124824, -2.1283458156}
Solution
x = {2.5450124824, -2.1283458156}