15n^2-22np-5p^2=

Solution for 15n^2-22np-5p^2= equation:

Simplifying
15n2 + -22np + -5p2 = 0

Reorder the terms:
-22np + 15n2 + -5p2 = 0

Solving
-22np + 15n2 + -5p2 = 0

Solving for variable 'n'.

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

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

Simplifying
3n + -5p = 0

Solving
3n + -5p = 0

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

Add '5p' to each side of the equation.
3n + -5p + 5p = 0 + 5p

Combine like terms: -5p + 5p = 0
3n + 0 = 0 + 5p
3n = 0 + 5p
Remove the zero:
3n = 5p

Divide each side by '3'.
n = 1.666666667p

Simplifying
n = 1.666666667p
Subproblem 2
Set the factor '(5n + p)' equal to zero and attempt to solve:

Simplifying
5n + p = 0

Solving
5n + p = 0

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

Add '-1p' to each side of the equation.
5n + p + -1p = 0 + -1p

Combine like terms: p + -1p = 0
5n + 0 = 0 + -1p
5n = 0 + -1p
Remove the zero:
5n = -1p

Divide each side by '5'.
n = -0.2p

Simplifying
n = -0.2p
Solution
n = {1.666666667p, -0.2p}