33w+90=-3w^2

Solution for 33w+90=-3w^2 equation:

Simplifying
33w + 90 = -3w2

Reorder the terms:
90 + 33w = -3w2

Solving
90 + 33w = -3w2

Solving for variable 'w'.

Combine like terms: -3w2 + 3w2 = 0
90 + 33w + 3w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(30 + 11w + w2) = 0

Factor a trinomial.
3((6 + w)(5 + w)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 0

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

Add '-6' to each side of the equation.
6 + -6 + w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + w = 0 + -6
w = 0 + -6

Combine like terms: 0 + -6 = -6
w = -6

Simplifying
w = -6
Subproblem 2
Set the factor '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

Solving
5 + w = 0

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

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

Combine like terms: 5 + -5 = 0
0 + w = 0 + -5
w = 0 + -5

Combine like terms: 0 + -5 = -5
w = -5

Simplifying
w = -5
Solution
w = {-6, -5}