4n^2=72+2n

Solution for 4n^2=72+2n equation:

Simplifying
4n2 = 72 + 2n

Solving
4n2 = 72 + 2n

Solving for variable 'n'.

Reorder the terms:
-72 + -2n + 4n2 = 72 + 2n + -72 + -2n

Reorder the terms:
-72 + -2n + 4n2 = 72 + -72 + 2n + -2n

Combine like terms: 72 + -72 = 0
-72 + -2n + 4n2 = 0 + 2n + -2n
-72 + -2n + 4n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
-72 + -2n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + -1n + 2n2) = 0

Factor a trinomial.
2((-4 + -1n)(9 + -2n)) = 0

Ignore the factor 2.
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 '(9 + -2n)' equal to zero and attempt to solve:

Simplifying
9 + -2n = 0

Solving
9 + -2n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2n = 0 + -9
-2n = 0 + -9

Combine like terms: 0 + -9 = -9
-2n = -9

Divide each side by '-2'.
n = 4.5

Simplifying
n = 4.5
Solution
n = {-4, 4.5}