-23=4(3x-7)(-8x-5)

Solution for -23=4(3x-7)(-8x-5) equation:

Simplifying
-23 = 4(3x + -7)(-8x + -5)

Reorder the terms:
-23 = 4(-7 + 3x)(-8x + -5)

Reorder the terms:
-23 = 4(-7 + 3x)(-5 + -8x)

Multiply (-7 + 3x) * (-5 + -8x)
-23 = 4(-7(-5 + -8x) + 3x * (-5 + -8x))
-23 = 4((-5 * -7 + -8x * -7) + 3x * (-5 + -8x))
-23 = 4((35 + 56x) + 3x * (-5 + -8x))
-23 = 4(35 + 56x + (-5 * 3x + -8x * 3x))
-23 = 4(35 + 56x + (-15x + -24x2))

Combine like terms: 56x + -15x = 41x
-23 = 4(35 + 41x + -24x2)
-23 = (35 * 4 + 41x * 4 + -24x2 * 4)
-23 = (140 + 164x + -96x2)

Solving
-23 = 140 + 164x + -96x2

Solving for variable 'x'.

Combine like terms: -23 + -140 = -163
-163 + -164x + 96x2 = 140 + 164x + -96x2 + -140 + -164x + 96x2

Reorder the terms:
-163 + -164x + 96x2 = 140 + -140 + 164x + -164x + -96x2 + 96x2

Combine like terms: 140 + -140 = 0
-163 + -164x + 96x2 = 0 + 164x + -164x + -96x2 + 96x2
-163 + -164x + 96x2 = 164x + -164x + -96x2 + 96x2

Combine like terms: 164x + -164x = 0
-163 + -164x + 96x2 = 0 + -96x2 + 96x2
-163 + -164x + 96x2 = -96x2 + 96x2

Combine like terms: -96x2 + 96x2 = 0
-163 + -164x + 96x2 = 0

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

Divide each side by '96'.
-1.697916667 + -1.708333333x + x2 = 0

Move the constant term to the right:

Add '1.697916667' to each side of the equation.
-1.697916667 + -1.708333333x + 1.697916667 + x2 = 0 + 1.697916667

Reorder the terms:
-1.697916667 + 1.697916667 + -1.708333333x + x2 = 0 + 1.697916667

Combine like terms: -1.697916667 + 1.697916667 = 0.000000000
0.000000000 + -1.708333333x + x2 = 0 + 1.697916667
-1.708333333x + x2 = 0 + 1.697916667

Combine like terms: 0 + 1.697916667 = 1.697916667
-1.708333333x + x2 = 1.697916667

The x term is -1.708333333x.  Take half its coefficient (-0.8541666665).
Square it (0.7296006942) and add it to both sides.

Add '0.7296006942' to each side of the equation.
-1.708333333x + 0.7296006942 + x2 = 1.697916667 + 0.7296006942

Reorder the terms:
0.7296006942 + -1.708333333x + x2 = 1.697916667 + 0.7296006942

Combine like terms: 1.697916667 + 0.7296006942 = 2.4275173612
0.7296006942 + -1.708333333x + x2 = 2.4275173612

Factor a perfect square on the left side:
(x + -0.8541666665)(x + -0.8541666665) = 2.4275173612

Calculate the square root of the right side: 1.558049217

Break this problem into two subproblems by setting 
(x + -0.8541666665) equal to 1.558049217 and -1.558049217.

Subproblem 1
x + -0.8541666665 = 1.558049217

Simplifying
x + -0.8541666665 = 1.558049217

Reorder the terms:
-0.8541666665 + x = 1.558049217

Solving
-0.8541666665 + x = 1.558049217

Solving for variable 'x'.

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

Add '0.8541666665' to each side of the equation.
-0.8541666665 + 0.8541666665 + x = 1.558049217 + 0.8541666665

Combine like terms: -0.8541666665 + 0.8541666665 = 0.0000000000
0.0000000000 + x = 1.558049217 + 0.8541666665
x = 1.558049217 + 0.8541666665

Combine like terms: 1.558049217 + 0.8541666665 = 2.4122158835
x = 2.4122158835

Simplifying
x = 2.4122158835

Subproblem 2
x + -0.8541666665 = -1.558049217

Simplifying
x + -0.8541666665 = -1.558049217

Reorder the terms:
-0.8541666665 + x = -1.558049217

Solving
-0.8541666665 + x = -1.558049217

Solving for variable 'x'.

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

Add '0.8541666665' to each side of the equation.
-0.8541666665 + 0.8541666665 + x = -1.558049217 + 0.8541666665

Combine like terms: -0.8541666665 + 0.8541666665 = 0.0000000000
0.0000000000 + x = -1.558049217 + 0.8541666665
x = -1.558049217 + 0.8541666665

Combine like terms: -1.558049217 + 0.8541666665 = -0.7038825505
x = -0.7038825505

Simplifying
x = -0.7038825505

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.4122158835, -0.7038825505}