2n^2=15+n

Solution for 2n^2=15+n equation:

Simplifying
2n2 = 15 + n

Solving
2n2 = 15 + n

Solving for variable 'n'.

Reorder the terms:
-15 + -1n + 2n2 = 15 + n + -15 + -1n

Reorder the terms:
-15 + -1n + 2n2 = 15 + -15 + n + -1n

Combine like terms: 15 + -15 = 0
-15 + -1n + 2n2 = 0 + n + -1n
-15 + -1n + 2n2 = n + -1n

Combine like terms: n + -1n = 0
-15 + -1n + 2n2 = 0

Factor a trinomial.
(-5 + -2n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-5 + -2n)' equal to zero and attempt to solve:

Simplifying
-5 + -2n = 0

Solving
-5 + -2n = 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 + -2n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2n = 0 + 5
-2n = 0 + 5

Combine like terms: 0 + 5 = 5
-2n = 5

Divide each side by '-2'.
n = -2.5

Simplifying
n = -2.5
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-2.5, 3}