x(x+8)=(x+5)(2x-8)

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Solution for x(x+8)=(x+5)(2x-8) equation: 


Simplifying
x(x + 8) = (x + 5)(2x + -8)

Reorder the terms:
x(8 + x) = (x + 5)(2x + -8)
(8 * x + x * x) = (x + 5)(2x + -8)
(8x + x2) = (x + 5)(2x + -8)

Reorder the terms:
8x + x2 = (5 + x)(2x + -8)

Reorder the terms:
8x + x2 = (5 + x)(-8 + 2x)

Multiply (5 + x) * (-8 + 2x)
8x + x2 = (5(-8 + 2x) + x(-8 + 2x))
8x + x2 = ((-8 * 5 + 2x * 5) + x(-8 + 2x))
8x + x2 = ((-40 + 10x) + x(-8 + 2x))
8x + x2 = (-40 + 10x + (-8 * x + 2x * x))
8x + x2 = (-40 + 10x + (-8x + 2x2))

Combine like terms: 10x + -8x = 2x
8x + x2 = (-40 + 2x + 2x2)

Solving
8x + x2 = -40 + 2x + 2x2

Solving for variable 'x'.

Reorder the terms:
40 + 8x + -2x + x2 + -2x2 = -40 + 2x + 2x2 + 40 + -2x + -2x2

Combine like terms: 8x + -2x = 6x
40 + 6x + x2 + -2x2 = -40 + 2x + 2x2 + 40 + -2x + -2x2

Combine like terms: x2 + -2x2 = -1x2
40 + 6x + -1x2 = -40 + 2x + 2x2 + 40 + -2x + -2x2

Reorder the terms:
40 + 6x + -1x2 = -40 + 40 + 2x + -2x + 2x2 + -2x2

Combine like terms: -40 + 40 = 0
40 + 6x + -1x2 = 0 + 2x + -2x + 2x2 + -2x2
40 + 6x + -1x2 = 2x + -2x + 2x2 + -2x2

Combine like terms: 2x + -2x = 0
40 + 6x + -1x2 = 0 + 2x2 + -2x2
40 + 6x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
40 + 6x + -1x2 = 0

Factor a trinomial.
(10 + -1x)(4 + x) = 0


Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

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

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

Divide each side by '-1'.
x = 10

Simplifying
x = 10

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 = {10, -4}

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