14x(2x-6)=3x(8x+8)

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Solution for 14x(2x-6)=3x(8x+8) equation: 


Simplifying
14x(2x + -6) = 3x(8x + 8)

Reorder the terms:
14x(-6 + 2x) = 3x(8x + 8)
(-6 * 14x + 2x * 14x) = 3x(8x + 8)
(-84x + 28x2) = 3x(8x + 8)

Reorder the terms:
-84x + 28x2 = 3x(8 + 8x)
-84x + 28x2 = (8 * 3x + 8x * 3x)
-84x + 28x2 = (24x + 24x2)

Solving
-84x + 28x2 = 24x + 24x2

Solving for variable 'x'.

Reorder the terms:
-84x + -24x + 28x2 + -24x2 = 24x + 24x2 + -24x + -24x2

Combine like terms: -84x + -24x = -108x
-108x + 28x2 + -24x2 = 24x + 24x2 + -24x + -24x2

Combine like terms: 28x2 + -24x2 = 4x2
-108x + 4x2 = 24x + 24x2 + -24x + -24x2

Reorder the terms:
-108x + 4x2 = 24x + -24x + 24x2 + -24x2

Combine like terms: 24x + -24x = 0
-108x + 4x2 = 0 + 24x2 + -24x2
-108x + 4x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
-108x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-27 + 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 '(-27 + x)' equal to zero and attempt to solve:

Simplifying
-27 + x = 0

Solving
-27 + x = 0

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

Add '27' to each side of the equation.
-27 + 27 + x = 0 + 27

Combine like terms: -27 + 27 = 0
0 + x = 0 + 27
x = 0 + 27

Combine like terms: 0 + 27 = 27
x = 27

Simplifying
x = 27
Solution
x = {0, 27}

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