(x-2)(x+6)-(4x-7)(x+5)=

Solution for (x-2)(x+6)-(4x-7)(x+5)= equation:

Simplifying
(x + -2)(x + 6) + -1(4x + -7)(x + 5) = 0

Reorder the terms:
(-2 + x)(x + 6) + -1(4x + -7)(x + 5) = 0

Reorder the terms:
(-2 + x)(6 + x) + -1(4x + -7)(x + 5) = 0

Multiply (-2 + x) * (6 + x)
(-2(6 + x) + x(6 + x)) + -1(4x + -7)(x + 5) = 0
((6 * -2 + x * -2) + x(6 + x)) + -1(4x + -7)(x + 5) = 0
((-12 + -2x) + x(6 + x)) + -1(4x + -7)(x + 5) = 0
(-12 + -2x + (6 * x + x * x)) + -1(4x + -7)(x + 5) = 0
(-12 + -2x + (6x + x2)) + -1(4x + -7)(x + 5) = 0

Combine like terms: -2x + 6x = 4x
(-12 + 4x + x2) + -1(4x + -7)(x + 5) = 0

Reorder the terms:
-12 + 4x + x2 + -1(-7 + 4x)(x + 5) = 0

Reorder the terms:
-12 + 4x + x2 + -1(-7 + 4x)(5 + x) = 0

Multiply (-7 + 4x) * (5 + x)
-12 + 4x + x2 + -1(-7(5 + x) + 4x * (5 + x)) = 0
-12 + 4x + x2 + -1((5 * -7 + x * -7) + 4x * (5 + x)) = 0
-12 + 4x + x2 + -1((-35 + -7x) + 4x * (5 + x)) = 0
-12 + 4x + x2 + -1(-35 + -7x + (5 * 4x + x * 4x)) = 0
-12 + 4x + x2 + -1(-35 + -7x + (20x + 4x2)) = 0

Combine like terms: -7x + 20x = 13x
-12 + 4x + x2 + -1(-35 + 13x + 4x2) = 0
-12 + 4x + x2 + (-35 * -1 + 13x * -1 + 4x2 * -1) = 0
-12 + 4x + x2 + (35 + -13x + -4x2) = 0

Reorder the terms:
-12 + 35 + 4x + -13x + x2 + -4x2 = 0

Combine like terms: -12 + 35 = 23
23 + 4x + -13x + x2 + -4x2 = 0

Combine like terms: 4x + -13x = -9x
23 + -9x + x2 + -4x2 = 0

Combine like terms: x2 + -4x2 = -3x2
23 + -9x + -3x2 = 0

Solving
23 + -9x + -3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-7.666666667 + 3x + x2 = 0

Move the constant term to the right:

Add '7.666666667' to each side of the equation.
-7.666666667 + 3x + 7.666666667 + x2 = 0 + 7.666666667

Reorder the terms:
-7.666666667 + 7.666666667 + 3x + x2 = 0 + 7.666666667

Combine like terms: -7.666666667 + 7.666666667 = 0.000000000
0.000000000 + 3x + x2 = 0 + 7.666666667
3x + x2 = 0 + 7.666666667

Combine like terms: 0 + 7.666666667 = 7.666666667
3x + x2 = 7.666666667

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 7.666666667 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 7.666666667 + 2.25

Combine like terms: 7.666666667 + 2.25 = 9.916666667
2.25 + 3x + x2 = 9.916666667

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 9.916666667

Calculate the square root of the right side: 3.149073938

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.149073938 and -3.149073938.

Subproblem 1
x + 1.5 = 3.149073938

Simplifying
x + 1.5 = 3.149073938

Reorder the terms:
1.5 + x = 3.149073938

Solving
1.5 + x = 3.149073938

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 3.149073938 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 3.149073938 + -1.5
x = 3.149073938 + -1.5

Combine like terms: 3.149073938 + -1.5 = 1.649073938
x = 1.649073938

Simplifying
x = 1.649073938

Subproblem 2
x + 1.5 = -3.149073938

Simplifying
x + 1.5 = -3.149073938

Reorder the terms:
1.5 + x = -3.149073938

Solving
1.5 + x = -3.149073938

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -3.149073938 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -3.149073938 + -1.5
x = -3.149073938 + -1.5

Combine like terms: -3.149073938 + -1.5 = -4.649073938
x = -4.649073938

Simplifying
x = -4.649073938

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.649073938, -4.649073938}