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

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

Simplifying
(x + 7)(x + -6) = (x + 7)

Reorder the terms:
(7 + x)(x + -6) = (x + 7)

Reorder the terms:
(7 + x)(-6 + x) = (x + 7)

Multiply (7 + x) * (-6 + x)
(7(-6 + x) + x(-6 + x)) = (x + 7)
((-6 * 7 + x * 7) + x(-6 + x)) = (x + 7)
((-42 + 7x) + x(-6 + x)) = (x + 7)
(-42 + 7x + (-6 * x + x * x)) = (x + 7)
(-42 + 7x + (-6x + x2)) = (x + 7)

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

Reorder the terms:
-42 + 1x + x2 = (7 + x)

Remove parenthesis around (7 + x)
-42 + 1x + x2 = 7 + x

Solving
-42 + 1x + x2 = 7 + x

Solving for variable 'x'.

Reorder the terms:
-42 + -7 + 1x + -1x + x2 = 7 + x + -7 + -1x

Combine like terms: -42 + -7 = -49
-49 + 1x + -1x + x2 = 7 + x + -7 + -1x

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

Reorder the terms:
-49 + x2 = 7 + -7 + x + -1x

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

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

Factor a difference between two squares.
(7 + x)(-7 + x) = 0

Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7
Solution
x = {-7, 7}