(x-5)(x+6)-(-7x-6)(x-8)=

Solution for (x-5)(x+6)-(-7x-6)(x-8)= equation:

Simplifying
(x + -5)(x + 6) + -1(-7x + -6)(x + -8) = 0

Reorder the terms:
(-5 + x)(x + 6) + -1(-7x + -6)(x + -8) = 0

Reorder the terms:
(-5 + x)(6 + x) + -1(-7x + -6)(x + -8) = 0

Multiply (-5 + x) * (6 + x)
(-5(6 + x) + x(6 + x)) + -1(-7x + -6)(x + -8) = 0
((6 * -5 + x * -5) + x(6 + x)) + -1(-7x + -6)(x + -8) = 0
((-30 + -5x) + x(6 + x)) + -1(-7x + -6)(x + -8) = 0
(-30 + -5x + (6 * x + x * x)) + -1(-7x + -6)(x + -8) = 0
(-30 + -5x + (6x + x2)) + -1(-7x + -6)(x + -8) = 0

Combine like terms: -5x + 6x = 1x
(-30 + 1x + x2) + -1(-7x + -6)(x + -8) = 0

Reorder the terms:
-30 + 1x + x2 + -1(-6 + -7x)(x + -8) = 0

Reorder the terms:
-30 + 1x + x2 + -1(-6 + -7x)(-8 + x) = 0

Multiply (-6 + -7x) * (-8 + x)
-30 + 1x + x2 + -1(-6(-8 + x) + -7x * (-8 + x)) = 0
-30 + 1x + x2 + -1((-8 * -6 + x * -6) + -7x * (-8 + x)) = 0
-30 + 1x + x2 + -1((48 + -6x) + -7x * (-8 + x)) = 0
-30 + 1x + x2 + -1(48 + -6x + (-8 * -7x + x * -7x)) = 0
-30 + 1x + x2 + -1(48 + -6x + (56x + -7x2)) = 0

Combine like terms: -6x + 56x = 50x
-30 + 1x + x2 + -1(48 + 50x + -7x2) = 0
-30 + 1x + x2 + (48 * -1 + 50x * -1 + -7x2 * -1) = 0
-30 + 1x + x2 + (-48 + -50x + 7x2) = 0

Reorder the terms:
-30 + -48 + 1x + -50x + x2 + 7x2 = 0

Combine like terms: -30 + -48 = -78
-78 + 1x + -50x + x2 + 7x2 = 0

Combine like terms: 1x + -50x = -49x
-78 + -49x + x2 + 7x2 = 0

Combine like terms: x2 + 7x2 = 8x2
-78 + -49x + 8x2 = 0

Solving
-78 + -49x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-9.75 + -6.125x + x2 = 0

Move the constant term to the right:

Add '9.75' to each side of the equation.
-9.75 + -6.125x + 9.75 + x2 = 0 + 9.75

Reorder the terms:
-9.75 + 9.75 + -6.125x + x2 = 0 + 9.75

Combine like terms: -9.75 + 9.75 = 0.00
0.00 + -6.125x + x2 = 0 + 9.75
-6.125x + x2 = 0 + 9.75

Combine like terms: 0 + 9.75 = 9.75
-6.125x + x2 = 9.75

The x term is -6.125x.  Take half its coefficient (-3.0625).
Square it (9.37890625) and add it to both sides.

Add '9.37890625' to each side of the equation.
-6.125x + 9.37890625 + x2 = 9.75 + 9.37890625

Reorder the terms:
9.37890625 + -6.125x + x2 = 9.75 + 9.37890625

Combine like terms: 9.75 + 9.37890625 = 19.12890625
9.37890625 + -6.125x + x2 = 19.12890625

Factor a perfect square on the left side:
(x + -3.0625)(x + -3.0625) = 19.12890625

Calculate the square root of the right side: 4.373660509

Break this problem into two subproblems by setting 
(x + -3.0625) equal to 4.373660509 and -4.373660509.

Subproblem 1
x + -3.0625 = 4.373660509

Simplifying
x + -3.0625 = 4.373660509

Reorder the terms:
-3.0625 + x = 4.373660509

Solving
-3.0625 + x = 4.373660509

Solving for variable 'x'.

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

Add '3.0625' to each side of the equation.
-3.0625 + 3.0625 + x = 4.373660509 + 3.0625

Combine like terms: -3.0625 + 3.0625 = 0.0000
0.0000 + x = 4.373660509 + 3.0625
x = 4.373660509 + 3.0625

Combine like terms: 4.373660509 + 3.0625 = 7.436160509
x = 7.436160509

Simplifying
x = 7.436160509

Subproblem 2
x + -3.0625 = -4.373660509

Simplifying
x + -3.0625 = -4.373660509

Reorder the terms:
-3.0625 + x = -4.373660509

Solving
-3.0625 + x = -4.373660509

Solving for variable 'x'.

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

Add '3.0625' to each side of the equation.
-3.0625 + 3.0625 + x = -4.373660509 + 3.0625

Combine like terms: -3.0625 + 3.0625 = 0.0000
0.0000 + x = -4.373660509 + 3.0625
x = -4.373660509 + 3.0625

Combine like terms: -4.373660509 + 3.0625 = -1.311160509
x = -1.311160509

Simplifying
x = -1.311160509

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.436160509, -1.311160509}