8x(x-3)-30=5x(x-5)

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Solution for 8x(x-3)-30=5x(x-5) equation: 


Simplifying
8x(x + -3) + -30 = 5x(x + -5)

Reorder the terms:
8x(-3 + x) + -30 = 5x(x + -5)
(-3 * 8x + x * 8x) + -30 = 5x(x + -5)
(-24x + 8x2) + -30 = 5x(x + -5)

Reorder the terms:
-30 + -24x + 8x2 = 5x(x + -5)

Reorder the terms:
-30 + -24x + 8x2 = 5x(-5 + x)
-30 + -24x + 8x2 = (-5 * 5x + x * 5x)
-30 + -24x + 8x2 = (-25x + 5x2)

Solving
-30 + -24x + 8x2 = -25x + 5x2

Solving for variable 'x'.

Reorder the terms:
-30 + -24x + 25x + 8x2 + -5x2 = -25x + 5x2 + 25x + -5x2

Combine like terms: -24x + 25x = 1x
-30 + 1x + 8x2 + -5x2 = -25x + 5x2 + 25x + -5x2

Combine like terms: 8x2 + -5x2 = 3x2
-30 + 1x + 3x2 = -25x + 5x2 + 25x + -5x2

Reorder the terms:
-30 + 1x + 3x2 = -25x + 25x + 5x2 + -5x2

Combine like terms: -25x + 25x = 0
-30 + 1x + 3x2 = 0 + 5x2 + -5x2
-30 + 1x + 3x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-30 + 1x + 3x2 = 0

Factor a trinomial.
(-10 + -3x)(3 + -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 '(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 = {-3.333333333, 3}

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