(x-1)(x+5)=(x+2)2-9

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Solution for (x-1)(x+5)=(x+2)2-9 equation: 


Simplifying
(x + -1)(x + 5) = (x + 2) * 2 + -9

Reorder the terms:
(-1 + x)(x + 5) = (x + 2) * 2 + -9

Reorder the terms:
(-1 + x)(5 + x) = (x + 2) * 2 + -9

Multiply (-1 + x) * (5 + x)
(-1(5 + x) + x(5 + x)) = (x + 2) * 2 + -9
((5 * -1 + x * -1) + x(5 + x)) = (x + 2) * 2 + -9
((-5 + -1x) + x(5 + x)) = (x + 2) * 2 + -9
(-5 + -1x + (5 * x + x * x)) = (x + 2) * 2 + -9
(-5 + -1x + (5x + x2)) = (x + 2) * 2 + -9

Combine like terms: -1x + 5x = 4x
(-5 + 4x + x2) = (x + 2) * 2 + -9

Reorder the terms:
-5 + 4x + x2 = (2 + x) * 2 + -9

Reorder the terms for easier multiplication:
-5 + 4x + x2 = 2(2 + x) + -9
-5 + 4x + x2 = (2 * 2 + x * 2) + -9
-5 + 4x + x2 = (4 + 2x) + -9

Reorder the terms:
-5 + 4x + x2 = 4 + -9 + 2x

Combine like terms: 4 + -9 = -5
-5 + 4x + x2 = -5 + 2x

Add '5' to each side of the equation.
-5 + 4x + 5 + x2 = -5 + 5 + 2x

Reorder the terms:
-5 + 5 + 4x + x2 = -5 + 5 + 2x

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

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

Solving
4x + x2 = 2x

Solving for variable 'x'.

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(2 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Solution
x = {0, -2}

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