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

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


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

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

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

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

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

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

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

Solving for variable 'x'.

Reorder the terms:
-40 + 2x + -8x + 2x2 + -1x2 = 8x + x2 + -8x + -1x2

Combine like terms: 2x + -8x = -6x
-40 + -6x + 2x2 + -1x2 = 8x + x2 + -8x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-40 + -6x + 1x2 = 8x + x2 + -8x + -1x2

Reorder the terms:
-40 + -6x + 1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
-40 + -6x + 1x2 = 0 + x2 + -1x2
-40 + -6x + 1x2 = x2 + -1x2

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

Factor a trinomial.
(-4 + -1x)(10 + -1x) = 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 '(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
Solution
x = {-4, 10}

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