(2x+11)(x-7)-(x+7)(12x+8)=0

Solution for (2x+11)(x-7)-(x+7)(12x+8)=0 equation:

Simplifying
(2x + 11)(x + -7) + -1(x + 7)(12x + 8) = 0

Reorder the terms:
(11 + 2x)(x + -7) + -1(x + 7)(12x + 8) = 0

Reorder the terms:
(11 + 2x)(-7 + x) + -1(x + 7)(12x + 8) = 0

Multiply (11 + 2x) * (-7 + x)
(11(-7 + x) + 2x * (-7 + x)) + -1(x + 7)(12x + 8) = 0
((-7 * 11 + x * 11) + 2x * (-7 + x)) + -1(x + 7)(12x + 8) = 0
((-77 + 11x) + 2x * (-7 + x)) + -1(x + 7)(12x + 8) = 0
(-77 + 11x + (-7 * 2x + x * 2x)) + -1(x + 7)(12x + 8) = 0
(-77 + 11x + (-14x + 2x2)) + -1(x + 7)(12x + 8) = 0

Combine like terms: 11x + -14x = -3x
(-77 + -3x + 2x2) + -1(x + 7)(12x + 8) = 0

Reorder the terms:
-77 + -3x + 2x2 + -1(7 + x)(12x + 8) = 0

Reorder the terms:
-77 + -3x + 2x2 + -1(7 + x)(8 + 12x) = 0

Multiply (7 + x) * (8 + 12x)
-77 + -3x + 2x2 + -1(7(8 + 12x) + x(8 + 12x)) = 0
-77 + -3x + 2x2 + -1((8 * 7 + 12x * 7) + x(8 + 12x)) = 0
-77 + -3x + 2x2 + -1((56 + 84x) + x(8 + 12x)) = 0
-77 + -3x + 2x2 + -1(56 + 84x + (8 * x + 12x * x)) = 0
-77 + -3x + 2x2 + -1(56 + 84x + (8x + 12x2)) = 0

Combine like terms: 84x + 8x = 92x
-77 + -3x + 2x2 + -1(56 + 92x + 12x2) = 0
-77 + -3x + 2x2 + (56 * -1 + 92x * -1 + 12x2 * -1) = 0
-77 + -3x + 2x2 + (-56 + -92x + -12x2) = 0

Reorder the terms:
-77 + -56 + -3x + -92x + 2x2 + -12x2 = 0

Combine like terms: -77 + -56 = -133
-133 + -3x + -92x + 2x2 + -12x2 = 0

Combine like terms: -3x + -92x = -95x
-133 + -95x + 2x2 + -12x2 = 0

Combine like terms: 2x2 + -12x2 = -10x2
-133 + -95x + -10x2 = 0

Solving
-133 + -95x + -10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(133 + 95x + 10x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(133 + 95x + 10x2)' equal to zero and attempt to solve:

Simplifying
133 + 95x + 10x2 = 0

Solving
133 + 95x + 10x2 = 0

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

Divide each side by '10'.
13.3 + 9.5x + x2 = 0.0

Move the constant term to the right:

Add '-13.3' to each side of the equation.
13.3 + 9.5x + -13.3 + x2 = 0.0 + -13.3

Reorder the terms:
13.3 + -13.3 + 9.5x + x2 = 0.0 + -13.3

Combine like terms: 13.3 + -13.3 = 0.0
0.0 + 9.5x + x2 = 0.0 + -13.3
9.5x + x2 = 0.0 + -13.3

Combine like terms: 0.0 + -13.3 = -13.3
9.5x + x2 = -13.3

The x term is 9.5x.  Take half its coefficient (4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
9.5x + 22.5625 + x2 = -13.3 + 22.5625

Reorder the terms:
22.5625 + 9.5x + x2 = -13.3 + 22.5625

Combine like terms: -13.3 + 22.5625 = 9.2625
22.5625 + 9.5x + x2 = 9.2625

Factor a perfect square on the left side:
(x + 4.75)(x + 4.75) = 9.2625

Calculate the square root of the right side: 3.043435559

Break this problem into two subproblems by setting 
(x + 4.75) equal to 3.043435559 and -3.043435559.

Subproblem 1
x + 4.75 = 3.043435559

Simplifying
x + 4.75 = 3.043435559

Reorder the terms:
4.75 + x = 3.043435559

Solving
4.75 + x = 3.043435559

Solving for variable 'x'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + x = 3.043435559 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + x = 3.043435559 + -4.75
x = 3.043435559 + -4.75

Combine like terms: 3.043435559 + -4.75 = -1.706564441
x = -1.706564441

Simplifying
x = -1.706564441

Subproblem 2
x + 4.75 = -3.043435559

Simplifying
x + 4.75 = -3.043435559

Reorder the terms:
4.75 + x = -3.043435559

Solving
4.75 + x = -3.043435559

Solving for variable 'x'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + x = -3.043435559 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + x = -3.043435559 + -4.75
x = -3.043435559 + -4.75

Combine like terms: -3.043435559 + -4.75 = -7.793435559
x = -7.793435559

Simplifying
x = -7.793435559

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.706564441, -7.793435559}
Solution
x = {-1.706564441, -7.793435559}