3x(x+12)=2x(2x+4)

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Solution for 3x(x+12)=2x(2x+4) equation: 


Simplifying
3x(x + 12) = 2x(2x + 4)

Reorder the terms:
3x(12 + x) = 2x(2x + 4)
(12 * 3x + x * 3x) = 2x(2x + 4)
(36x + 3x2) = 2x(2x + 4)

Reorder the terms:
36x + 3x2 = 2x(4 + 2x)
36x + 3x2 = (4 * 2x + 2x * 2x)
36x + 3x2 = (8x + 4x2)

Solving
36x + 3x2 = 8x + 4x2

Solving for variable 'x'.

Reorder the terms:
36x + -8x + 3x2 + -4x2 = 8x + 4x2 + -8x + -4x2

Combine like terms: 36x + -8x = 28x
28x + 3x2 + -4x2 = 8x + 4x2 + -8x + -4x2

Combine like terms: 3x2 + -4x2 = -1x2
28x + -1x2 = 8x + 4x2 + -8x + -4x2

Reorder the terms:
28x + -1x2 = 8x + -8x + 4x2 + -4x2

Combine like terms: 8x + -8x = 0
28x + -1x2 = 0 + 4x2 + -4x2
28x + -1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
28x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(28 + -1x) = 0


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 '(28 + -1x)' equal to zero and attempt to solve:

Simplifying
28 + -1x = 0

Solving
28 + -1x = 0

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

Add '-28' to each side of the equation.
28 + -28 + -1x = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -1x = 0 + -28
-1x = 0 + -28

Combine like terms: 0 + -28 = -28
-1x = -28

Divide each side by '-1'.
x = 28

Simplifying
x = 28
Solution
x = {0, 28}

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