3x(2x-8)=2x(-4x+16)

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Solution for 3x(2x-8)=2x(-4x+16) equation: 


Simplifying
3x(2x + -8) = 2x(-4x + 16)

Reorder the terms:
3x(-8 + 2x) = 2x(-4x + 16)
(-8 * 3x + 2x * 3x) = 2x(-4x + 16)
(-24x + 6x2) = 2x(-4x + 16)

Reorder the terms:
-24x + 6x2 = 2x(16 + -4x)
-24x + 6x2 = (16 * 2x + -4x * 2x)
-24x + 6x2 = (32x + -8x2)

Solving
-24x + 6x2 = 32x + -8x2

Solving for variable 'x'.

Reorder the terms:
-24x + -32x + 6x2 + 8x2 = 32x + -8x2 + -32x + 8x2

Combine like terms: -24x + -32x = -56x
-56x + 6x2 + 8x2 = 32x + -8x2 + -32x + 8x2

Combine like terms: 6x2 + 8x2 = 14x2
-56x + 14x2 = 32x + -8x2 + -32x + 8x2

Reorder the terms:
-56x + 14x2 = 32x + -32x + -8x2 + 8x2

Combine like terms: 32x + -32x = 0
-56x + 14x2 = 0 + -8x2 + 8x2
-56x + 14x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
-56x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '14x'.
14x(-4 + x) = 0

Ignore the factor 14.

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 '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
Solution
x = {0, 4}

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