x(x+1)(2x+5)=0

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Solution for x(x+1)(2x+5)=0 equation: 


Simplifying
x(x + 1)(2x + 5) = 0

Reorder the terms:
x(1 + x)(2x + 5) = 0

Reorder the terms:
x(1 + x)(5 + 2x) = 0

Multiply (1 + x) * (5 + 2x)
x(1(5 + 2x) + x(5 + 2x)) = 0
x((5 * 1 + 2x * 1) + x(5 + 2x)) = 0
x((5 + 2x) + x(5 + 2x)) = 0
x(5 + 2x + (5 * x + 2x * x)) = 0
x(5 + 2x + (5x + 2x2)) = 0

Combine like terms: 2x + 5x = 7x
x(5 + 7x + 2x2) = 0
(5 * x + 7x * x + 2x2 * x) = 0
(5x + 7x2 + 2x3) = 0

Solving
5x + 7x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + 7x + 2x2) = 0

Factor a trinomial.
x((5 + 2x)(1 + x)) = 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 '(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

Subproblem 3
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {0, -2.5, -1}

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