n^2(n+2)(2n+5)=0

Solution for n^2(n+2)(2n+5)=0 equation:

Simplifying
n2(n + 2)(2n + 5) = 0

Reorder the terms:
n2(2 + n)(2n + 5) = 0

Reorder the terms:
n2(2 + n)(5 + 2n) = 0

Multiply (2 + n) * (5 + 2n)
n2(2(5 + 2n) + n(5 + 2n)) = 0
n2((5 * 2 + 2n * 2) + n(5 + 2n)) = 0
n2((10 + 4n) + n(5 + 2n)) = 0
n2(10 + 4n + (5 * n + 2n * n)) = 0
n2(10 + 4n + (5n + 2n2)) = 0

Combine like terms: 4n + 5n = 9n
n2(10 + 9n + 2n2) = 0
(10 * n2 + 9n * n2 + 2n2 * n2) = 0
(10n2 + 9n3 + 2n4) = 0

Solving
10n2 + 9n3 + 2n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n2'.
n2(10 + 9n + 2n2) = 0

Factor a trinomial.
n2((5 + 2n)(2 + n)) = 0

Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve:

Simplifying
n2 = 0

Solving
n2 = 0

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

Simplifying
n2 = 0

Take the square root of each side:
n = {0}
Subproblem 2
Set the factor '(5 + 2n)' equal to zero and attempt to solve:

Simplifying
5 + 2n = 0

Solving
5 + 2n = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2n = 0 + -5

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

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

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

Simplifying
n = -2.5
Subproblem 3
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + n = 0 + -2
n = 0 + -2

Combine like terms: 0 + -2 = -2
n = -2

Simplifying
n = -2
Solution
n = {0, -2.5, -2}