2n^2+72=24n

Solution for 2n^2+72=24n equation:

Simplifying
2n2 + 72 = 24n

Reorder the terms:
72 + 2n2 = 24n

Solving
72 + 2n2 = 24n

Solving for variable 'n'.

Reorder the terms:
72 + -24n + 2n2 = 24n + -24n

Combine like terms: 24n + -24n = 0
72 + -24n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + -12n + n2) = 0

Factor a trinomial.
2((6 + -1n)(6 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {6, 6}