(4x)(6x-20)=(5x)(4x+8)

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Solution for (4x)(6x-20)=(5x)(4x+8) equation: 


Simplifying
(4x)(6x + -20) = (5x)(4x + 8)

Remove parenthesis around (4x)
4x(6x + -20) = (5x)(4x + 8)

Reorder the terms:
4x(-20 + 6x) = (5x)(4x + 8)
(-20 * 4x + 6x * 4x) = (5x)(4x + 8)
(-80x + 24x2) = (5x)(4x + 8)

Remove parenthesis around (5x)
-80x + 24x2 = 5x(4x + 8)

Reorder the terms:
-80x + 24x2 = 5x(8 + 4x)
-80x + 24x2 = (8 * 5x + 4x * 5x)
-80x + 24x2 = (40x + 20x2)

Solving
-80x + 24x2 = 40x + 20x2

Solving for variable 'x'.

Reorder the terms:
-80x + -40x + 24x2 + -20x2 = 40x + 20x2 + -40x + -20x2

Combine like terms: -80x + -40x = -120x
-120x + 24x2 + -20x2 = 40x + 20x2 + -40x + -20x2

Combine like terms: 24x2 + -20x2 = 4x2
-120x + 4x2 = 40x + 20x2 + -40x + -20x2

Reorder the terms:
-120x + 4x2 = 40x + -40x + 20x2 + -20x2

Combine like terms: 40x + -40x = 0
-120x + 4x2 = 0 + 20x2 + -20x2
-120x + 4x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
-120x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-30 + x) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-30 + x)' equal to zero and attempt to solve:

Simplifying
-30 + x = 0

Solving
-30 + x = 0

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

Add '30' to each side of the equation.
-30 + 30 + x = 0 + 30

Combine like terms: -30 + 30 = 0
0 + x = 0 + 30
x = 0 + 30

Combine like terms: 0 + 30 = 30
x = 30

Simplifying
x = 30
Solution
x = {0, 30}

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