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

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


Simplifying
x(2x + 4)(6 + -1x) = 0

Reorder the terms:
x(4 + 2x)(6 + -1x) = 0

Multiply (4 + 2x) * (6 + -1x)
x(4(6 + -1x) + 2x * (6 + -1x)) = 0
x((6 * 4 + -1x * 4) + 2x * (6 + -1x)) = 0
x((24 + -4x) + 2x * (6 + -1x)) = 0
x(24 + -4x + (6 * 2x + -1x * 2x)) = 0
x(24 + -4x + (12x + -2x2)) = 0

Combine like terms: -4x + 12x = 8x
x(24 + 8x + -2x2) = 0
(24 * x + 8x * x + -2x2 * x) = 0
(24x + 8x2 + -2x3) = 0

Solving
24x + 8x2 + -2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(12 + 4x + -1x2) = 0

Factor a trinomial.
2x((6 + -1x)(2 + 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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {0, 6, -2}

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