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

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


Simplifying
(x + 6)(x + -5) = x + 6

Reorder the terms:
(6 + x)(x + -5) = x + 6

Reorder the terms:
(6 + x)(-5 + x) = x + 6

Multiply (6 + x) * (-5 + x)
(6(-5 + x) + x(-5 + x)) = x + 6
((-5 * 6 + x * 6) + x(-5 + x)) = x + 6
((-30 + 6x) + x(-5 + x)) = x + 6
(-30 + 6x + (-5 * x + x * x)) = x + 6
(-30 + 6x + (-5x + x2)) = x + 6

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

Reorder the terms:
-30 + 1x + x2 = 6 + x

Solving
-30 + 1x + x2 = 6 + x

Solving for variable 'x'.

Reorder the terms:
-30 + -6 + 1x + -1x + x2 = 6 + x + -6 + -1x

Combine like terms: -30 + -6 = -36
-36 + 1x + -1x + x2 = 6 + x + -6 + -1x

Combine like terms: 1x + -1x = 0
-36 + 0 + x2 = 6 + x + -6 + -1x
-36 + x2 = 6 + x + -6 + -1x

Reorder the terms:
-36 + x2 = 6 + -6 + x + -1x

Combine like terms: 6 + -6 = 0
-36 + x2 = 0 + x + -1x
-36 + x2 = x + -1x

Combine like terms: x + -1x = 0
-36 + x2 = 0

Factor a difference between two squares.
(6 + x)(-6 + x) = 0


Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

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

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

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

Simplifying
x = -6

Subproblem 2
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

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

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

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
Solution
x = {-6, 6}

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