2n^2=84-2n

Solution for 2n^2=84-2n equation:

Simplifying
2n2 = 84 + -2n

Solving
2n2 = 84 + -2n

Solving for variable 'n'.

Reorder the terms:
-84 + 2n + 2n2 = 84 + -2n + -84 + 2n

Reorder the terms:
-84 + 2n + 2n2 = 84 + -84 + -2n + 2n

Combine like terms: 84 + -84 = 0
-84 + 2n + 2n2 = 0 + -2n + 2n
-84 + 2n + 2n2 = -2n + 2n

Combine like terms: -2n + 2n = 0
-84 + 2n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-42 + n + n2) = 0

Factor a trinomial.
2((-7 + -1n)(6 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7
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 = {-7, 6}