(2n^2-10)+(n+6)=32

Solution for (2n^2-10)+(n+6)=32 equation:

Simplifying
(2n2 + -10) + (n + 6) = 32

Reorder the terms:
(-10 + 2n2) + (n + 6) = 32

Remove parenthesis around (-10 + 2n2)
-10 + 2n2 + (n + 6) = 32

Reorder the terms:
-10 + 2n2 + (6 + n) = 32

Remove parenthesis around (6 + n)
-10 + 2n2 + 6 + n = 32

Reorder the terms:
-10 + 6 + n + 2n2 = 32

Combine like terms: -10 + 6 = -4
-4 + n + 2n2 = 32

Solving
-4 + n + 2n2 = 32

Solving for variable 'n'.

Reorder the terms:
-4 + -32 + n + 2n2 = 32 + -32

Combine like terms: -4 + -32 = -36
-36 + n + 2n2 = 32 + -32

Combine like terms: 32 + -32 = 0
-36 + n + 2n2 = 0

Factor a trinomial.
(-9 + -2n)(4 + -1n) = 0

Subproblem 1
Set the factor '(-9 + -2n)' equal to zero and attempt to solve:

Simplifying
-9 + -2n = 0

Solving
-9 + -2n = 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 + -2n = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2n = 0 + 9
-2n = 0 + 9

Combine like terms: 0 + 9 = 9
-2n = 9

Divide each side by '-2'.
n = -4.5

Simplifying
n = -4.5
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-4.5, 4}