15n^2+13n=20

Solution for 15n^2+13n=20 equation:

Simplifying
15n2 + 13n = 20

Reorder the terms:
13n + 15n2 = 20

Solving
13n + 15n2 = 20

Solving for variable 'n'.

Reorder the terms:
-20 + 13n + 15n2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 13n + 15n2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
n = {-1.666666667, 0.8}