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

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


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

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

Combine like terms: 4x + -6x = -2x
2x(12 + -2x + -2x2) = 0
(12 * 2x + -2x * 2x + -2x2 * 2x) = 0
(24x + -4x2 + -4x3) = 0

Solving
24x + -4x2 + -4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(6 + -1x + -1x2) = 0

Factor a trinomial.
4x((2 + -1x)(3 + x)) = 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 '(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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