x(x+4)(2x+5)=0

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Solution for x(x+4)(2x+5)=0 equation: 


Simplifying
x(x + 4)(2x + 5) = 0

Reorder the terms:
x(4 + x)(2x + 5) = 0

Reorder the terms:
x(4 + x)(5 + 2x) = 0

Multiply (4 + x) * (5 + 2x)
x(4(5 + 2x) + x(5 + 2x)) = 0
x((5 * 4 + 2x * 4) + x(5 + 2x)) = 0
x((20 + 8x) + x(5 + 2x)) = 0
x(20 + 8x + (5 * x + 2x * x)) = 0
x(20 + 8x + (5x + 2x2)) = 0

Combine like terms: 8x + 5x = 13x
x(20 + 13x + 2x2) = 0
(20 * x + 13x * x + 2x2 * x) = 0
(20x + 13x2 + 2x3) = 0

Solving
20x + 13x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(20 + 13x + 2x2) = 0

Factor a trinomial.
x((4 + x)(5 + 2x)) = 0


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 '(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 '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {0, -4, -2.5}

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