6x+2x(x+3)=4x(x-3)

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Solution for 6x+2x(x+3)=4x(x-3) equation: 


Simplifying
6x + 2x(x + 3) = 4x(x + -3)

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

Combine like terms: 6x + 6x = 12x
12x + 2x2 = 4x(x + -3)

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

Solving
12x + 2x2 = -12x + 4x2

Solving for variable 'x'.

Reorder the terms:
12x + 12x + 2x2 + -4x2 = -12x + 4x2 + 12x + -4x2

Combine like terms: 12x + 12x = 24x
24x + 2x2 + -4x2 = -12x + 4x2 + 12x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
24x + -2x2 = -12x + 4x2 + 12x + -4x2

Reorder the terms:
24x + -2x2 = -12x + 12x + 4x2 + -4x2

Combine like terms: -12x + 12x = 0
24x + -2x2 = 0 + 4x2 + -4x2
24x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
24x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(12 + -1x) = 0

Ignore the factor 2.

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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {0, 12}

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