(x+2)*(x-2)=2*(x+5)+21

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Solution for (x+2)*(x-2)=2*(x+5)+21 equation: 


Simplifying
(x + 2)(x + -2) = 2(x + 5) + 21

Reorder the terms:
(2 + x)(x + -2) = 2(x + 5) + 21

Reorder the terms:
(2 + x)(-2 + x) = 2(x + 5) + 21

Multiply (2 + x) * (-2 + x)
(2(-2 + x) + x(-2 + x)) = 2(x + 5) + 21
((-2 * 2 + x * 2) + x(-2 + x)) = 2(x + 5) + 21
((-4 + 2x) + x(-2 + x)) = 2(x + 5) + 21
(-4 + 2x + (-2 * x + x * x)) = 2(x + 5) + 21
(-4 + 2x + (-2x + x2)) = 2(x + 5) + 21

Combine like terms: 2x + -2x = 0
(-4 + 0 + x2) = 2(x + 5) + 21
(-4 + x2) = 2(x + 5) + 21

Reorder the terms:
-4 + x2 = 2(5 + x) + 21
-4 + x2 = (5 * 2 + x * 2) + 21
-4 + x2 = (10 + 2x) + 21

Reorder the terms:
-4 + x2 = 10 + 21 + 2x

Combine like terms: 10 + 21 = 31
-4 + x2 = 31 + 2x

Solving
-4 + x2 = 31 + 2x

Solving for variable 'x'.

Reorder the terms:
-4 + -31 + -2x + x2 = 31 + 2x + -31 + -2x

Combine like terms: -4 + -31 = -35
-35 + -2x + x2 = 31 + 2x + -31 + -2x

Reorder the terms:
-35 + -2x + x2 = 31 + -31 + 2x + -2x

Combine like terms: 31 + -31 = 0
-35 + -2x + x2 = 0 + 2x + -2x
-35 + -2x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-35 + -2x + x2 = 0

Factor a trinomial.
(-5 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

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

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

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-5, 7}

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