2x(x+4)(6-3x)=0

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Solution for 2x(x+4)(6-3x)=0 equation: 


Simplifying
2x(x + 4)(6 + -3x) = 0

Reorder the terms:
2x(4 + x)(6 + -3x) = 0

Multiply (4 + x) * (6 + -3x)
2x(4(6 + -3x) + x(6 + -3x)) = 0
2x((6 * 4 + -3x * 4) + x(6 + -3x)) = 0
2x((24 + -12x) + x(6 + -3x)) = 0
2x(24 + -12x + (6 * x + -3x * x)) = 0
2x(24 + -12x + (6x + -3x2)) = 0

Combine like terms: -12x + 6x = -6x
2x(24 + -6x + -3x2) = 0
(24 * 2x + -6x * 2x + -3x2 * 2x) = 0
(48x + -12x2 + -6x3) = 0

Solving
48x + -12x2 + -6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(8 + -2x + -1x2) = 0

Factor a trinomial.
6x((2 + -1x)(4 + x)) = 0

Ignore the factor 6.

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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {0, 2, -4}

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