x(x+5)=(2x+10)(x-2)

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Solution for x(x+5)=(2x+10)(x-2) equation: 


Simplifying
x(x + 5) = (2x + 10)(x + -2)

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

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

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

Multiply (10 + 2x) * (-2 + x)
5x + x2 = (10(-2 + x) + 2x * (-2 + x))
5x + x2 = ((-2 * 10 + x * 10) + 2x * (-2 + x))
5x + x2 = ((-20 + 10x) + 2x * (-2 + x))
5x + x2 = (-20 + 10x + (-2 * 2x + x * 2x))
5x + x2 = (-20 + 10x + (-4x + 2x2))

Combine like terms: 10x + -4x = 6x
5x + x2 = (-20 + 6x + 2x2)

Solving
5x + x2 = -20 + 6x + 2x2

Solving for variable 'x'.

Reorder the terms:
20 + 5x + -6x + x2 + -2x2 = -20 + 6x + 2x2 + 20 + -6x + -2x2

Combine like terms: 5x + -6x = -1x
20 + -1x + x2 + -2x2 = -20 + 6x + 2x2 + 20 + -6x + -2x2

Combine like terms: x2 + -2x2 = -1x2
20 + -1x + -1x2 = -20 + 6x + 2x2 + 20 + -6x + -2x2

Reorder the terms:
20 + -1x + -1x2 = -20 + 20 + 6x + -6x + 2x2 + -2x2

Combine like terms: -20 + 20 = 0
20 + -1x + -1x2 = 0 + 6x + -6x + 2x2 + -2x2
20 + -1x + -1x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
20 + -1x + -1x2 = 0 + 2x2 + -2x2
20 + -1x + -1x2 = 2x2 + -2x2

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

Factor a trinomial.
(4 + -1x)(5 + x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

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

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