n^2=32+4n

Solution for n^2=32+4n equation:

Simplifying
n2 = 32 + 4n

Solving
n2 = 32 + 4n

Solving for variable 'n'.

Reorder the terms:
-32 + -4n + n2 = 32 + 4n + -32 + -4n

Reorder the terms:
-32 + -4n + n2 = 32 + -32 + 4n + -4n

Combine like terms: 32 + -32 = 0
-32 + -4n + n2 = 0 + 4n + -4n
-32 + -4n + n2 = 4n + -4n

Combine like terms: 4n + -4n = 0
-32 + -4n + n2 = 0

Factor a trinomial.
(-4 + -1n)(8 + -1n) = 0

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 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 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 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 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {-4, 8}