(x^2+4x)(x^2+5x)=

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Solution for (x^2+4x)(x^2+5x)= equation: 


Simplifying
(x2 + 4x)(x2 + 5x) = 0

Reorder the terms:
(4x + x2)(x2 + 5x) = 0

Reorder the terms:
(4x + x2)(5x + x2) = 0

Multiply (4x + x2) * (5x + x2)
(4x * (5x + x2) + x2(5x + x2)) = 0
((5x * 4x + x2 * 4x) + x2(5x + x2)) = 0
((20x2 + 4x3) + x2(5x + x2)) = 0
(20x2 + 4x3 + (5x * x2 + x2 * x2)) = 0
(20x2 + 4x3 + (5x3 + x4)) = 0

Combine like terms: 4x3 + 5x3 = 9x3
(20x2 + 9x3 + x4) = 0

Solving
20x2 + 9x3 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(20 + 9x + x2) = 0

Factor a trinomial.
x2((5 + x)(4 + x)) = 0


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

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5

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, -5, -4}

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