15n^2-48=22n

Solution for 15n^2-48=22n equation:

Simplifying
15n2 + -48 = 22n

Reorder the terms:
-48 + 15n2 = 22n

Solving
-48 + 15n2 = 22n

Solving for variable 'n'.

Reorder the terms:
-48 + -22n + 15n2 = 22n + -22n

Combine like terms: 22n + -22n = 0
-48 + -22n + 15n2 = 0

Factor a trinomial.
(-6 + -5n)(8 + -3n) = 0

Subproblem 1
Set the factor '(-6 + -5n)' equal to zero and attempt to solve:

Simplifying
-6 + -5n = 0

Solving
-6 + -5n = 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 + -5n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5n = 0 + 6
-5n = 0 + 6

Combine like terms: 0 + 6 = 6
-5n = 6

Divide each side by '-5'.
n = -1.2

Simplifying
n = -1.2
Subproblem 2
Set the factor '(8 + -3n)' equal to zero and attempt to solve:

Simplifying
8 + -3n = 0

Solving
8 + -3n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3n = 0 + -8
-3n = 0 + -8

Combine like terms: 0 + -8 = -8
-3n = -8

Divide each side by '-3'.
n = 2.666666667

Simplifying
n = 2.666666667
Solution
n = {-1.2, 2.666666667}