2n^2=10n+72

Solution for 2n^2=10n+72 equation:

Simplifying
2n2 = 10n + 72

Reorder the terms:
2n2 = 72 + 10n

Solving
2n2 = 72 + 10n

Solving for variable 'n'.

Reorder the terms:
-72 + -10n + 2n2 = 72 + 10n + -72 + -10n

Reorder the terms:
-72 + -10n + 2n2 = 72 + -72 + 10n + -10n

Combine like terms: 72 + -72 = 0
-72 + -10n + 2n2 = 0 + 10n + -10n
-72 + -10n + 2n2 = 10n + -10n

Combine like terms: 10n + -10n = 0
-72 + -10n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + -5n + n2) = 0

Factor a trinomial.
2((-4 + -1n)(9 + -1n)) = 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 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 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 + -1n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1n = 0 + -9
-1n = 0 + -9

Combine like terms: 0 + -9 = -9
-1n = -9

Divide each side by '-1'.
n = 9

Simplifying
n = 9
Solution
n = {-4, 9}