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

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


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

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

Remove parenthesis around (2x)
6x + 6x2 = 2 * 2x(3 + -2x)

Multiply 2 * 2
6x + 6x2 = 4x(3 + -2x)
6x + 6x2 = (3 * 4x + -2x * 4x)
6x + 6x2 = (12x + -8x2)

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

Solving for variable 'x'.

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

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

Combine like terms: 6x2 + 8x2 = 14x2
-6x + 14x2 = 12x + -8x2 + -12x + 8x2

Reorder the terms:
-6x + 14x2 = 12x + -12x + -8x2 + 8x2

Combine like terms: 12x + -12x = 0
-6x + 14x2 = 0 + -8x2 + 8x2
-6x + 14x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
-6x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-3 + 7x) = 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 '(-3 + 7x)' equal to zero and attempt to solve:

Simplifying
-3 + 7x = 0

Solving
-3 + 7x = 0

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

Add '3' to each side of the equation.
-3 + 3 + 7x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 7x = 0 + 3
7x = 0 + 3

Combine like terms: 0 + 3 = 3
7x = 3

Divide each side by '7'.
x = 0.4285714286

Simplifying
x = 0.4285714286
Solution
x = {0, 0.4285714286}

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