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

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


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

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

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

Multiply (-2 + x) * (5 + x)
(-2(5 + x) + x(5 + x)) = x + -2(x + 5)
((5 * -2 + x * -2) + x(5 + x)) = x + -2(x + 5)
((-10 + -2x) + x(5 + x)) = x + -2(x + 5)
(-10 + -2x + (5 * x + x * x)) = x + -2(x + 5)
(-10 + -2x + (5x + x2)) = x + -2(x + 5)

Combine like terms: -2x + 5x = 3x
(-10 + 3x + x2) = x + -2(x + 5)

Reorder the terms:
-10 + 3x + x2 = x + -2(5 + x)
-10 + 3x + x2 = x + (5 * -2 + x * -2)
-10 + 3x + x2 = x + (-10 + -2x)

Reorder the terms:
-10 + 3x + x2 = -10 + x + -2x

Combine like terms: x + -2x = -1x
-10 + 3x + x2 = -10 + -1x

Add '10' to each side of the equation.
-10 + 3x + 10 + x2 = -10 + 10 + -1x

Reorder the terms:
-10 + 10 + 3x + x2 = -10 + 10 + -1x

Combine like terms: -10 + 10 = 0
0 + 3x + x2 = -10 + 10 + -1x
3x + x2 = -10 + 10 + -1x

Combine like terms: -10 + 10 = 0
3x + x2 = 0 + -1x
3x + x2 = -1x

Solving
3x + x2 = -1x

Solving for variable 'x'.

Reorder the terms:
3x + x + x2 = -1x + x

Combine like terms: 3x + x = 4x
4x + x2 = -1x + x

Combine like terms: -1x + x = 0
4x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(4 + 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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {0, -4}

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