(x^3+4x^2)(-9x-36)=0

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Solution for (x^3+4x^2)(-9x-36)=0 equation: 


Simplifying
(x3 + 4x2)(-9x + -36) = 0

Reorder the terms:
(4x2 + x3)(-9x + -36) = 0

Reorder the terms:
(4x2 + x3)(-36 + -9x) = 0

Multiply (4x2 + x3) * (-36 + -9x)
(4x2 * (-36 + -9x) + x3(-36 + -9x)) = 0
((-36 * 4x2 + -9x * 4x2) + x3(-36 + -9x)) = 0
((-144x2 + -36x3) + x3(-36 + -9x)) = 0
(-144x2 + -36x3 + (-36 * x3 + -9x * x3)) = 0
(-144x2 + -36x3 + (-36x3 + -9x4)) = 0

Combine like terms: -36x3 + -36x3 = -72x3
(-144x2 + -72x3 + -9x4) = 0

Solving
-144x2 + -72x3 + -9x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-9x2'.
-9x2(16 + 8x + x2) = 0

Factor a trinomial.
-9x2((4 + x)(4 + x)) = 0

Ignore the factor -9.

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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