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

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


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

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

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

Solving
12x + -2x2 + -2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(6 + -1x + -1x2) = 0

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

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {0, 2, -3}

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