5n^2-6n=32

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

Simplifying
5n2 + -6n = 32

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

Solving
-6n + 5n2 = 32

Solving for variable 'n'.

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

Combine like terms: 32 + -32 = 0
-32 + -6n + 5n2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
n = {-2, 3.2}