5n^2-32n=21

Solution for 5n^2-32n=21 equation:

Simplifying
5n2 + -32n = 21

Reorder the terms:
-32n + 5n2 = 21

Solving
-32n + 5n2 = 21

Solving for variable 'n'.

Reorder the terms:
-21 + -32n + 5n2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -32n + 5n2 = 0

Factor a trinomial.
(-3 + -5n)(7 + -1n) = 0

Subproblem 1
Set the factor '(-3 + -5n)' equal to zero and attempt to solve:

Simplifying
-3 + -5n = 0

Solving
-3 + -5n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -5n = 0 + 3

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

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

Divide each side by '-5'.
n = -0.6

Simplifying
n = -0.6
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {-0.6, 7}