15n^2-22n=5

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

Simplifying
15n2 + -22n = 5

Reorder the terms:
-22n + 15n2 = 5

Solving
-22n + 15n2 = 5

Solving for variable 'n'.

Reorder the terms:
-5 + -22n + 15n2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -22n + 15n2 = 0

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

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

Simplifying
-1 + -5n = 0

Solving
-1 + -5n = 0

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

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

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

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

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

Simplifying
n = -0.2
Subproblem 2
Set the factor '(5 + -3n)' equal to zero and attempt to solve:

Simplifying
5 + -3n = 0

Solving
5 + -3n = 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 + -3n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3n = 0 + -5
-3n = 0 + -5

Combine like terms: 0 + -5 = -5
-3n = -5

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

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