8x(x-5)-50=5x(x-7)

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Solution for 8x(x-5)-50=5x(x-7) equation: 


Simplifying
8x(x + -5) + -50 = 5x(x + -7)

Reorder the terms:
8x(-5 + x) + -50 = 5x(x + -7)
(-5 * 8x + x * 8x) + -50 = 5x(x + -7)
(-40x + 8x2) + -50 = 5x(x + -7)

Reorder the terms:
-50 + -40x + 8x2 = 5x(x + -7)

Reorder the terms:
-50 + -40x + 8x2 = 5x(-7 + x)
-50 + -40x + 8x2 = (-7 * 5x + x * 5x)
-50 + -40x + 8x2 = (-35x + 5x2)

Solving
-50 + -40x + 8x2 = -35x + 5x2

Solving for variable 'x'.

Reorder the terms:
-50 + -40x + 35x + 8x2 + -5x2 = -35x + 5x2 + 35x + -5x2

Combine like terms: -40x + 35x = -5x
-50 + -5x + 8x2 + -5x2 = -35x + 5x2 + 35x + -5x2

Combine like terms: 8x2 + -5x2 = 3x2
-50 + -5x + 3x2 = -35x + 5x2 + 35x + -5x2

Reorder the terms:
-50 + -5x + 3x2 = -35x + 35x + 5x2 + -5x2

Combine like terms: -35x + 35x = 0
-50 + -5x + 3x2 = 0 + 5x2 + -5x2
-50 + -5x + 3x2 = 5x2 + -5x2

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

Factor a trinomial.
(-10 + -3x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-10 + -3x)' equal to zero and attempt to solve:

Simplifying
-10 + -3x = 0

Solving
-10 + -3x = 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 + -3x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3x = 0 + 10
-3x = 0 + 10

Combine like terms: 0 + 10 = 10
-3x = 10

Divide each side by '-3'.
x = -3.333333333

Simplifying
x = -3.333333333

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 = {-3.333333333, 5}

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