4n^2+33n=-8

Solution for 4n^2+33n=-8 equation:

Simplifying
4n2 + 33n = -8

Reorder the terms:
33n + 4n2 = -8

Solving
33n + 4n2 = -8

Solving for variable 'n'.

Reorder the terms:
8 + 33n + 4n2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + 33n + 4n2 = 0

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

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 + 4n)' equal to zero and attempt to solve:

Simplifying
1 + 4n = 0

Solving
1 + 4n = 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 + 4n = 0 + -1

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

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

Divide each side by '4'.
n = -0.25

Simplifying
n = -0.25
Solution
n = {-8, -0.25}