5x(x+5)=(4x-8)(x+5)

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Solution for 5x(x+5)=(4x-8)(x+5) equation: 


Simplifying
5x(x + 5) = (4x + -8)(x + 5)

Reorder the terms:
5x(5 + x) = (4x + -8)(x + 5)
(5 * 5x + x * 5x) = (4x + -8)(x + 5)
(25x + 5x2) = (4x + -8)(x + 5)

Reorder the terms:
25x + 5x2 = (-8 + 4x)(x + 5)

Reorder the terms:
25x + 5x2 = (-8 + 4x)(5 + x)

Multiply (-8 + 4x) * (5 + x)
25x + 5x2 = (-8(5 + x) + 4x * (5 + x))
25x + 5x2 = ((5 * -8 + x * -8) + 4x * (5 + x))
25x + 5x2 = ((-40 + -8x) + 4x * (5 + x))
25x + 5x2 = (-40 + -8x + (5 * 4x + x * 4x))
25x + 5x2 = (-40 + -8x + (20x + 4x2))

Combine like terms: -8x + 20x = 12x
25x + 5x2 = (-40 + 12x + 4x2)

Solving
25x + 5x2 = -40 + 12x + 4x2

Solving for variable 'x'.

Reorder the terms:
40 + 25x + -12x + 5x2 + -4x2 = -40 + 12x + 4x2 + 40 + -12x + -4x2

Combine like terms: 25x + -12x = 13x
40 + 13x + 5x2 + -4x2 = -40 + 12x + 4x2 + 40 + -12x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
40 + 13x + 1x2 = -40 + 12x + 4x2 + 40 + -12x + -4x2

Reorder the terms:
40 + 13x + 1x2 = -40 + 40 + 12x + -12x + 4x2 + -4x2

Combine like terms: -40 + 40 = 0
40 + 13x + 1x2 = 0 + 12x + -12x + 4x2 + -4x2
40 + 13x + 1x2 = 12x + -12x + 4x2 + -4x2

Combine like terms: 12x + -12x = 0
40 + 13x + 1x2 = 0 + 4x2 + -4x2
40 + 13x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
40 + 13x + 1x2 = 0

Factor a trinomial.
(8 + x)(5 + x) = 0


Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8

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 = {-8, -5}

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