8x(x-2)-50=5x(x-7)

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Solution for 8x(x-2)-50=5x(x-7) equation: 


Simplifying
8x(x + -2) + -50 = 5x(x + -7)

Reorder the terms:
8x(-2 + x) + -50 = 5x(x + -7)
(-2 * 8x + x * 8x) + -50 = 5x(x + -7)
(-16x + 8x2) + -50 = 5x(x + -7)

Reorder the terms:
-50 + -16x + 8x2 = 5x(x + -7)

Reorder the terms:
-50 + -16x + 8x2 = 5x(-7 + x)
-50 + -16x + 8x2 = (-7 * 5x + x * 5x)
-50 + -16x + 8x2 = (-35x + 5x2)

Solving
-50 + -16x + 8x2 = -35x + 5x2

Solving for variable 'x'.

Reorder the terms:
-50 + -16x + 35x + 8x2 + -5x2 = -35x + 5x2 + 35x + -5x2

Combine like terms: -16x + 35x = 19x
-50 + 19x + 8x2 + -5x2 = -35x + 5x2 + 35x + -5x2

Combine like terms: 8x2 + -5x2 = 3x2
-50 + 19x + 3x2 = -35x + 5x2 + 35x + -5x2

Reorder the terms:
-50 + 19x + 3x2 = -35x + 35x + 5x2 + -5x2

Combine like terms: -35x + 35x = 0
-50 + 19x + 3x2 = 0 + 5x2 + -5x2
-50 + 19x + 3x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-50 + 19x + 3x2 = 0

Factor a trinomial.
(-25 + -3x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-8.333333333, 2}

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