2n^2=144+(2n)

Solution for 2n^2=144+(2n) equation:

Simplifying
2n2 = 144 + (2n)

Solving
2n2 = 144 + (2n)

Solving for variable 'n'.

Reorder the terms:
-144 + (-2n) + 2n2 = 144 + (2n) + -144 + (-2n)

Reorder the terms:
-144 + (-2n) + 2n2 = 144 + -144 + (2n) + (-2n)

Combine like terms: 144 + -144 = 0
-144 + (-2n) + 2n2 = 0 + (2n) + (-2n)
-144 + (-2n) + 2n2 = (2n) + (-2n)

Combine like terms: (2n) + (-2n) = 0
-144 + (-2n) + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-72 + (-1n) + n2) = 0

Factor a trinomial.
2((-8 + -1n)(9 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {-8, 9}