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

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

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

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

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

Multiply (7 + x) * (-8 + x)
(7(-8 + x) + x(-8 + x)) + -1(5x + -7)(x + 6) = 0
((-8 * 7 + x * 7) + x(-8 + x)) + -1(5x + -7)(x + 6) = 0
((-56 + 7x) + x(-8 + x)) + -1(5x + -7)(x + 6) = 0
(-56 + 7x + (-8 * x + x * x)) + -1(5x + -7)(x + 6) = 0
(-56 + 7x + (-8x + x2)) + -1(5x + -7)(x + 6) = 0

Combine like terms: 7x + -8x = -1x
(-56 + -1x + x2) + -1(5x + -7)(x + 6) = 0

Reorder the terms:
-56 + -1x + x2 + -1(-7 + 5x)(x + 6) = 0

Reorder the terms:
-56 + -1x + x2 + -1(-7 + 5x)(6 + x) = 0

Multiply (-7 + 5x) * (6 + x)
-56 + -1x + x2 + -1(-7(6 + x) + 5x * (6 + x)) = 0
-56 + -1x + x2 + -1((6 * -7 + x * -7) + 5x * (6 + x)) = 0
-56 + -1x + x2 + -1((-42 + -7x) + 5x * (6 + x)) = 0
-56 + -1x + x2 + -1(-42 + -7x + (6 * 5x + x * 5x)) = 0
-56 + -1x + x2 + -1(-42 + -7x + (30x + 5x2)) = 0

Combine like terms: -7x + 30x = 23x
-56 + -1x + x2 + -1(-42 + 23x + 5x2) = 0
-56 + -1x + x2 + (-42 * -1 + 23x * -1 + 5x2 * -1) = 0
-56 + -1x + x2 + (42 + -23x + -5x2) = 0

Reorder the terms:
-56 + 42 + -1x + -23x + x2 + -5x2 = 0

Combine like terms: -56 + 42 = -14
-14 + -1x + -23x + x2 + -5x2 = 0

Combine like terms: -1x + -23x = -24x
-14 + -24x + x2 + -5x2 = 0

Combine like terms: x2 + -5x2 = -4x2
-14 + -24x + -4x2 = 0

Solving
-14 + -24x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(7 + 12x + 2x2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(7 + 12x + 2x2)' equal to zero and attempt to solve:

Simplifying
7 + 12x + 2x2 = 0

Solving
7 + 12x + 2x2 = 0

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

Divide each side by '2'.
3.5 + 6x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 6x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 6x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 6x + x2 = 0 + -3.5
6x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
6x + x2 = -3.5

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -3.5 + 9

Reorder the terms:
9 + 6x + x2 = -3.5 + 9

Combine like terms: -3.5 + 9 = 5.5
9 + 6x + x2 = 5.5

Factor a perfect square on the left side:
(x + 3)(x + 3) = 5.5

Calculate the square root of the right side: 2.34520788

Break this problem into two subproblems by setting 
(x + 3) equal to 2.34520788 and -2.34520788.

Subproblem 1
x + 3 = 2.34520788

Simplifying
x + 3 = 2.34520788

Reorder the terms:
3 + x = 2.34520788

Solving
3 + x = 2.34520788

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 2.34520788 + -3

Combine like terms: 3 + -3 = 0
0 + x = 2.34520788 + -3
x = 2.34520788 + -3

Combine like terms: 2.34520788 + -3 = -0.65479212
x = -0.65479212

Simplifying
x = -0.65479212

Subproblem 2
x + 3 = -2.34520788

Simplifying
x + 3 = -2.34520788

Reorder the terms:
3 + x = -2.34520788

Solving
3 + x = -2.34520788

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -2.34520788 + -3

Combine like terms: 3 + -3 = 0
0 + x = -2.34520788 + -3
x = -2.34520788 + -3

Combine like terms: -2.34520788 + -3 = -5.34520788
x = -5.34520788

Simplifying
x = -5.34520788

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.65479212, -5.34520788}
Solution
x = {-0.65479212, -5.34520788}