6x(2x-8)=2x(4x+12)

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Solution for 6x(2x-8)=2x(4x+12) equation: 


Simplifying
6x(2x + -8) = 2x(4x + 12)

Reorder the terms:
6x(-8 + 2x) = 2x(4x + 12)
(-8 * 6x + 2x * 6x) = 2x(4x + 12)
(-48x + 12x2) = 2x(4x + 12)

Reorder the terms:
-48x + 12x2 = 2x(12 + 4x)
-48x + 12x2 = (12 * 2x + 4x * 2x)
-48x + 12x2 = (24x + 8x2)

Solving
-48x + 12x2 = 24x + 8x2

Solving for variable 'x'.

Reorder the terms:
-48x + -24x + 12x2 + -8x2 = 24x + 8x2 + -24x + -8x2

Combine like terms: -48x + -24x = -72x
-72x + 12x2 + -8x2 = 24x + 8x2 + -24x + -8x2

Combine like terms: 12x2 + -8x2 = 4x2
-72x + 4x2 = 24x + 8x2 + -24x + -8x2

Reorder the terms:
-72x + 4x2 = 24x + -24x + 8x2 + -8x2

Combine like terms: 24x + -24x = 0
-72x + 4x2 = 0 + 8x2 + -8x2
-72x + 4x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-72x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-18 + 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 '(-18 + x)' equal to zero and attempt to solve:

Simplifying
-18 + x = 0

Solving
-18 + x = 0

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

Add '18' to each side of the equation.
-18 + 18 + x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + x = 0 + 18
x = 0 + 18

Combine like terms: 0 + 18 = 18
x = 18

Simplifying
x = 18
Solution
x = {0, 18}

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