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

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


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

Reorder the terms:
5x(-5 + x) = (2x + 8)(x + -5)
(-5 * 5x + x * 5x) = (2x + 8)(x + -5)
(-25x + 5x2) = (2x + 8)(x + -5)

Reorder the terms:
-25x + 5x2 = (8 + 2x)(x + -5)

Reorder the terms:
-25x + 5x2 = (8 + 2x)(-5 + x)

Multiply (8 + 2x) * (-5 + x)
-25x + 5x2 = (8(-5 + x) + 2x * (-5 + x))
-25x + 5x2 = ((-5 * 8 + x * 8) + 2x * (-5 + x))
-25x + 5x2 = ((-40 + 8x) + 2x * (-5 + x))
-25x + 5x2 = (-40 + 8x + (-5 * 2x + x * 2x))
-25x + 5x2 = (-40 + 8x + (-10x + 2x2))

Combine like terms: 8x + -10x = -2x
-25x + 5x2 = (-40 + -2x + 2x2)

Solving
-25x + 5x2 = -40 + -2x + 2x2

Solving for variable 'x'.

Reorder the terms:
40 + -25x + 2x + 5x2 + -2x2 = -40 + -2x + 2x2 + 40 + 2x + -2x2

Combine like terms: -25x + 2x = -23x
40 + -23x + 5x2 + -2x2 = -40 + -2x + 2x2 + 40 + 2x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
40 + -23x + 3x2 = -40 + -2x + 2x2 + 40 + 2x + -2x2

Reorder the terms:
40 + -23x + 3x2 = -40 + 40 + -2x + 2x + 2x2 + -2x2

Combine like terms: -40 + 40 = 0
40 + -23x + 3x2 = 0 + -2x + 2x + 2x2 + -2x2
40 + -23x + 3x2 = -2x + 2x + 2x2 + -2x2

Combine like terms: -2x + 2x = 0
40 + -23x + 3x2 = 0 + 2x2 + -2x2
40 + -23x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
40 + -23x + 3x2 = 0

Factor a trinomial.
(8 + -3x)(5 + -1x) = 0


Subproblem 1
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 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 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667

Subproblem 2
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
Solution
x = {2.666666667, 5}

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