2n^2+84=26n

Solution for 2n^2+84=26n equation:

Simplifying
2n2 + 84 = 26n

Reorder the terms:
84 + 2n2 = 26n

Solving
84 + 2n2 = 26n

Solving for variable 'n'.

Reorder the terms:
84 + -26n + 2n2 = 26n + -26n

Combine like terms: 26n + -26n = 0
84 + -26n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(42 + -13n + n2) = 0

Factor a trinomial.
2((6 + -1n)(7 + -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 '(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
Solution
n = {6, 7}