20n^2+5n^3=60n

Solution for 20n^2+5n^3=60n equation:

Simplifying
20n2 + 5n3 = 60n

Solving
20n2 + 5n3 = 60n

Solving for variable 'n'.

Reorder the terms:
-60n + 20n2 + 5n3 = 60n + -60n

Combine like terms: 60n + -60n = 0
-60n + 20n2 + 5n3 = 0

Factor out the Greatest Common Factor (GCF), '5n'.
5n(-12 + 4n + n2) = 0

Factor a trinomial.
5n((-6 + -1n)(2 + -1n)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 3
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {0, -6, 2}