(2x^3+8x^2)(3x+12)=

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Solution for (2x^3+8x^2)(3x+12)= equation: 


Simplifying
(2x3 + 8x2)(3x + 12) = 0

Reorder the terms:
(8x2 + 2x3)(3x + 12) = 0

Reorder the terms:
(8x2 + 2x3)(12 + 3x) = 0

Multiply (8x2 + 2x3) * (12 + 3x)
(8x2 * (12 + 3x) + 2x3 * (12 + 3x)) = 0
((12 * 8x2 + 3x * 8x2) + 2x3 * (12 + 3x)) = 0
((96x2 + 24x3) + 2x3 * (12 + 3x)) = 0
(96x2 + 24x3 + (12 * 2x3 + 3x * 2x3)) = 0
(96x2 + 24x3 + (24x3 + 6x4)) = 0

Combine like terms: 24x3 + 24x3 = 48x3
(96x2 + 48x3 + 6x4) = 0

Solving
96x2 + 48x3 + 6x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x2'.
6x2(16 + 8x + x2) = 0

Factor a trinomial.
6x2((4 + x)(4 + x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
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

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, -4, -4}

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