5n^2=72+2n

Solution for 5n^2=72+2n equation:

Simplifying
5n2 = 72 + 2n

Solving
5n2 = 72 + 2n

Solving for variable 'n'.

Reorder the terms:
-72 + -2n + 5n2 = 72 + 2n + -72 + -2n

Reorder the terms:
-72 + -2n + 5n2 = 72 + -72 + 2n + -2n

Combine like terms: 72 + -72 = 0
-72 + -2n + 5n2 = 0 + 2n + -2n
-72 + -2n + 5n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
-72 + -2n + 5n2 = 0

Factor a trinomial.
(-18 + -5n)(4 + -1n) = 0

Subproblem 1
Set the factor '(-18 + -5n)' equal to zero and attempt to solve:

Simplifying
-18 + -5n = 0

Solving
-18 + -5n = 0

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

Add '18' to each side of the equation.
-18 + 18 + -5n = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -5n = 0 + 18
-5n = 0 + 18

Combine like terms: 0 + 18 = 18
-5n = 18

Divide each side by '-5'.
n = -3.6

Simplifying
n = -3.6
Subproblem 2
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
Solution
n = {-3.6, 4}