(x-7)(x+6)-(2x+9)(x-6)=

Solution for (x-7)(x+6)-(2x+9)(x-6)= equation:

Simplifying
(x + -7)(x + 6) + -1(2x + 9)(x + -6) = 0

Reorder the terms:
(-7 + x)(x + 6) + -1(2x + 9)(x + -6) = 0

Reorder the terms:
(-7 + x)(6 + x) + -1(2x + 9)(x + -6) = 0

Multiply (-7 + x) * (6 + x)
(-7(6 + x) + x(6 + x)) + -1(2x + 9)(x + -6) = 0
((6 * -7 + x * -7) + x(6 + x)) + -1(2x + 9)(x + -6) = 0
((-42 + -7x) + x(6 + x)) + -1(2x + 9)(x + -6) = 0
(-42 + -7x + (6 * x + x * x)) + -1(2x + 9)(x + -6) = 0
(-42 + -7x + (6x + x2)) + -1(2x + 9)(x + -6) = 0

Combine like terms: -7x + 6x = -1x
(-42 + -1x + x2) + -1(2x + 9)(x + -6) = 0

Reorder the terms:
-42 + -1x + x2 + -1(9 + 2x)(x + -6) = 0

Reorder the terms:
-42 + -1x + x2 + -1(9 + 2x)(-6 + x) = 0

Multiply (9 + 2x) * (-6 + x)
-42 + -1x + x2 + -1(9(-6 + x) + 2x * (-6 + x)) = 0
-42 + -1x + x2 + -1((-6 * 9 + x * 9) + 2x * (-6 + x)) = 0
-42 + -1x + x2 + -1((-54 + 9x) + 2x * (-6 + x)) = 0
-42 + -1x + x2 + -1(-54 + 9x + (-6 * 2x + x * 2x)) = 0
-42 + -1x + x2 + -1(-54 + 9x + (-12x + 2x2)) = 0

Combine like terms: 9x + -12x = -3x
-42 + -1x + x2 + -1(-54 + -3x + 2x2) = 0
-42 + -1x + x2 + (-54 * -1 + -3x * -1 + 2x2 * -1) = 0
-42 + -1x + x2 + (54 + 3x + -2x2) = 0

Reorder the terms:
-42 + 54 + -1x + 3x + x2 + -2x2 = 0

Combine like terms: -42 + 54 = 12
12 + -1x + 3x + x2 + -2x2 = 0

Combine like terms: -1x + 3x = 2x
12 + 2x + x2 + -2x2 = 0

Combine like terms: x2 + -2x2 = -1x2
12 + 2x + -1x2 = 0

Solving
12 + 2x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-12 + -2x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -2x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -2x + x2 = 0 + 12

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

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

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 12 + 1

Reorder the terms:
1 + -2x + x2 = 12 + 1

Combine like terms: 12 + 1 = 13
1 + -2x + x2 = 13

Factor a perfect square on the left side:
(x + -1)(x + -1) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -1) equal to 3.605551275 and -3.605551275.

Subproblem 1
x + -1 = 3.605551275

Simplifying
x + -1 = 3.605551275

Reorder the terms:
-1 + x = 3.605551275

Solving
-1 + x = 3.605551275

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 3.605551275 + 1

Combine like terms: -1 + 1 = 0
0 + x = 3.605551275 + 1
x = 3.605551275 + 1

Combine like terms: 3.605551275 + 1 = 4.605551275
x = 4.605551275

Simplifying
x = 4.605551275

Subproblem 2
x + -1 = -3.605551275

Simplifying
x + -1 = -3.605551275

Reorder the terms:
-1 + x = -3.605551275

Solving
-1 + x = -3.605551275

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -3.605551275 + 1

Combine like terms: -1 + 1 = 0
0 + x = -3.605551275 + 1
x = -3.605551275 + 1

Combine like terms: -3.605551275 + 1 = -2.605551275
x = -2.605551275

Simplifying
x = -2.605551275

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.605551275, -2.605551275}