33=5w+2w^2

Solution for 33=5w+2w^2 equation:

Simplifying
33 = 5w + 2w2

Solving
33 = 5w + 2w2

Solving for variable 'w'.

Reorder the terms:
33 + -5w + -2w2 = 5w + -5w + 2w2 + -2w2

Combine like terms: 5w + -5w = 0
33 + -5w + -2w2 = 0 + 2w2 + -2w2
33 + -5w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
33 + -5w + -2w2 = 0

Factor a trinomial.
(3 + -1w)(11 + 2w) = 0

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

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

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

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

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

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

Simplifying
w = 3
Subproblem 2
Set the factor '(11 + 2w)' equal to zero and attempt to solve:

Simplifying
11 + 2w = 0

Solving
11 + 2w = 0

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

Add '-11' to each side of the equation.
11 + -11 + 2w = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 2w = 0 + -11
2w = 0 + -11

Combine like terms: 0 + -11 = -11
2w = -11

Divide each side by '2'.
w = -5.5

Simplifying
w = -5.5
Solution
w = {3, -5.5}