8x(x-5)-125=5x(x-10)

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Solution for 8x(x-5)-125=5x(x-10) equation: 


Simplifying
8x(x + -5) + -125 = 5x(x + -10)

Reorder the terms:
8x(-5 + x) + -125 = 5x(x + -10)
(-5 * 8x + x * 8x) + -125 = 5x(x + -10)
(-40x + 8x2) + -125 = 5x(x + -10)

Reorder the terms:
-125 + -40x + 8x2 = 5x(x + -10)

Reorder the terms:
-125 + -40x + 8x2 = 5x(-10 + x)
-125 + -40x + 8x2 = (-10 * 5x + x * 5x)
-125 + -40x + 8x2 = (-50x + 5x2)

Solving
-125 + -40x + 8x2 = -50x + 5x2

Solving for variable 'x'.

Reorder the terms:
-125 + -40x + 50x + 8x2 + -5x2 = -50x + 5x2 + 50x + -5x2

Combine like terms: -40x + 50x = 10x
-125 + 10x + 8x2 + -5x2 = -50x + 5x2 + 50x + -5x2

Combine like terms: 8x2 + -5x2 = 3x2
-125 + 10x + 3x2 = -50x + 5x2 + 50x + -5x2

Reorder the terms:
-125 + 10x + 3x2 = -50x + 50x + 5x2 + -5x2

Combine like terms: -50x + 50x = 0
-125 + 10x + 3x2 = 0 + 5x2 + -5x2
-125 + 10x + 3x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-125 + 10x + 3x2 = 0

Factor a trinomial.
(-25 + -3x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-25 + -3x)' equal to zero and attempt to solve:

Simplifying
-25 + -3x = 0

Solving
-25 + -3x = 0

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

Add '25' to each side of the equation.
-25 + 25 + -3x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -3x = 0 + 25
-3x = 0 + 25

Combine like terms: 0 + 25 = 25
-3x = 25

Divide each side by '-3'.
x = -8.333333333

Simplifying
x = -8.333333333

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 = {-8.333333333, 5}

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