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

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


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

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

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

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

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

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

Solving
-10 + 3x + x2 = 10 + 2x

Solving for variable 'x'.

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

Combine like terms: -10 + -10 = -20
-20 + 3x + -2x + x2 = 10 + 2x + -10 + -2x

Combine like terms: 3x + -2x = 1x
-20 + 1x + x2 = 10 + 2x + -10 + -2x

Reorder the terms:
-20 + 1x + x2 = 10 + -10 + 2x + -2x

Combine like terms: 10 + -10 = 0
-20 + 1x + x2 = 0 + 2x + -2x
-20 + 1x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-20 + 1x + x2 = 0

Factor a trinomial.
(-5 + -1x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-5, 4}

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