8x(x-3)-75=5x(x-8)

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Solution for 8x(x-3)-75=5x(x-8) equation: 


Simplifying
8x(x + -3) + -75 = 5x(x + -8)

Reorder the terms:
8x(-3 + x) + -75 = 5x(x + -8)
(-3 * 8x + x * 8x) + -75 = 5x(x + -8)
(-24x + 8x2) + -75 = 5x(x + -8)

Reorder the terms:
-75 + -24x + 8x2 = 5x(x + -8)

Reorder the terms:
-75 + -24x + 8x2 = 5x(-8 + x)
-75 + -24x + 8x2 = (-8 * 5x + x * 5x)
-75 + -24x + 8x2 = (-40x + 5x2)

Solving
-75 + -24x + 8x2 = -40x + 5x2

Solving for variable 'x'.

Reorder the terms:
-75 + -24x + 40x + 8x2 + -5x2 = -40x + 5x2 + 40x + -5x2

Combine like terms: -24x + 40x = 16x
-75 + 16x + 8x2 + -5x2 = -40x + 5x2 + 40x + -5x2

Combine like terms: 8x2 + -5x2 = 3x2
-75 + 16x + 3x2 = -40x + 5x2 + 40x + -5x2

Reorder the terms:
-75 + 16x + 3x2 = -40x + 40x + 5x2 + -5x2

Combine like terms: -40x + 40x = 0
-75 + 16x + 3x2 = 0 + 5x2 + -5x2
-75 + 16x + 3x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-75 + 16x + 3x2 = 0

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-8.333333333, 3}

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