n^2=2n+35

Solution for n^2=2n+35 equation:

Simplifying
n2 = 2n + 35

Reorder the terms:
n2 = 35 + 2n

Solving
n2 = 35 + 2n

Solving for variable 'n'.

Reorder the terms:
-35 + -2n + n2 = 35 + 2n + -35 + -2n

Reorder the terms:
-35 + -2n + n2 = 35 + -35 + 2n + -2n

Combine like terms: 35 + -35 = 0
-35 + -2n + n2 = 0 + 2n + -2n
-35 + -2n + n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
-35 + -2n + n2 = 0

Factor a trinomial.
(-5 + -1n)(7 + -1n) = 0

Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve:

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5
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 = {-5, 7}