4x(3x-2)=2x(3x+14)

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Solution for 4x(3x-2)=2x(3x+14) equation: 


Simplifying
4x(3x + -2) = 2x(3x + 14)

Reorder the terms:
4x(-2 + 3x) = 2x(3x + 14)
(-2 * 4x + 3x * 4x) = 2x(3x + 14)
(-8x + 12x2) = 2x(3x + 14)

Reorder the terms:
-8x + 12x2 = 2x(14 + 3x)
-8x + 12x2 = (14 * 2x + 3x * 2x)
-8x + 12x2 = (28x + 6x2)

Solving
-8x + 12x2 = 28x + 6x2

Solving for variable 'x'.

Reorder the terms:
-8x + -28x + 12x2 + -6x2 = 28x + 6x2 + -28x + -6x2

Combine like terms: -8x + -28x = -36x
-36x + 12x2 + -6x2 = 28x + 6x2 + -28x + -6x2

Combine like terms: 12x2 + -6x2 = 6x2
-36x + 6x2 = 28x + 6x2 + -28x + -6x2

Reorder the terms:
-36x + 6x2 = 28x + -28x + 6x2 + -6x2

Combine like terms: 28x + -28x = 0
-36x + 6x2 = 0 + 6x2 + -6x2
-36x + 6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-36x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-6 + x) = 0

Ignore the factor 6.

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 '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
Solution
x = {0, 6}

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