32=-4n^2-36n

Solution for 32=-4n^2-36n equation:

Simplifying
32 = -4n2 + -36n

Reorder the terms:
32 = -36n + -4n2

Solving
32 = -36n + -4n2

Solving for variable 'n'.

Reorder the terms:
32 + 36n + 4n2 = -36n + 36n + -4n2 + 4n2

Combine like terms: -36n + 36n = 0
32 + 36n + 4n2 = 0 + -4n2 + 4n2
32 + 36n + 4n2 = -4n2 + 4n2

Combine like terms: -4n2 + 4n2 = 0
32 + 36n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + 9n + n2) = 0

Factor a trinomial.
4((8 + n)(1 + n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve:

Simplifying
8 + n = 0

Solving
8 + n = 0

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

Add '-8' to each side of the equation.
8 + -8 + n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + n = 0 + -8
n = 0 + -8

Combine like terms: 0 + -8 = -8
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

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

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

Simplifying
n = -1
Solution
n = {-8, -1}