2x(3x+1)(4-2x)=0

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Solution for 2x(3x+1)(4-2x)=0 equation: 


Simplifying
2x(3x + 1)(4 + -2x) = 0

Reorder the terms:
2x(1 + 3x)(4 + -2x) = 0

Multiply (1 + 3x) * (4 + -2x)
2x(1(4 + -2x) + 3x * (4 + -2x)) = 0
2x((4 * 1 + -2x * 1) + 3x * (4 + -2x)) = 0
2x((4 + -2x) + 3x * (4 + -2x)) = 0
2x(4 + -2x + (4 * 3x + -2x * 3x)) = 0
2x(4 + -2x + (12x + -6x2)) = 0

Combine like terms: -2x + 12x = 10x
2x(4 + 10x + -6x2) = 0
(4 * 2x + 10x * 2x + -6x2 * 2x) = 0
(8x + 20x2 + -12x3) = 0

Solving
8x + 20x2 + -12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(2 + 5x + -3x2) = 0

Factor a trinomial.
4x((2 + -1x)(1 + 3x)) = 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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 3
Set the factor '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {0, 2, -0.3333333333}

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