15n^2+60=87n

Solution for 15n^2+60=87n equation:

Simplifying
15n2 + 60 = 87n

Reorder the terms:
60 + 15n2 = 87n

Solving
60 + 15n2 = 87n

Solving for variable 'n'.

Reorder the terms:
60 + -87n + 15n2 = 87n + -87n

Combine like terms: 87n + -87n = 0
60 + -87n + 15n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + -29n + 5n2) = 0

Factor a trinomial.
3((4 + -5n)(5 + -1n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + -5n)' equal to zero and attempt to solve:

Simplifying
4 + -5n = 0

Solving
4 + -5n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5n = 0 + -4
-5n = 0 + -4

Combine like terms: 0 + -4 = -4
-5n = -4

Divide each side by '-5'.
n = 0.8

Simplifying
n = 0.8
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 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 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {0.8, 5}