5n^2+6n-32=0

Solution for 5n^2+6n-32=0 equation:

Simplifying
5n2 + 6n + -32 = 0

Reorder the terms:
-32 + 6n + 5n2 = 0

Solving
-32 + 6n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-16 + -5n)(2 + -1n) = 0

Subproblem 1
Set the factor '(-16 + -5n)' equal to zero and attempt to solve:

Simplifying
-16 + -5n = 0

Solving
-16 + -5n = 0

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

Add '16' to each side of the equation.
-16 + 16 + -5n = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -5n = 0 + 16
-5n = 0 + 16

Combine like terms: 0 + 16 = 16
-5n = 16

Divide each side by '-5'.
n = -3.2

Simplifying
n = -3.2
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-3.2, 2}