10w^2+37w+33=0

Solution for 10w^2+37w+33=0 equation:

Simplifying
10w2 + 37w + 33 = 0

Reorder the terms:
33 + 37w + 10w2 = 0

Solving
33 + 37w + 10w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(11 + 5w)(3 + 2w) = 0

Subproblem 1
Set the factor '(11 + 5w)' equal to zero and attempt to solve:

Simplifying
11 + 5w = 0

Solving
11 + 5w = 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 + 5w = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 5w = 0 + -11
5w = 0 + -11

Combine like terms: 0 + -11 = -11
5w = -11

Divide each side by '5'.
w = -2.2

Simplifying
w = -2.2
Subproblem 2
Set the factor '(3 + 2w)' equal to zero and attempt to solve:

Simplifying
3 + 2w = 0

Solving
3 + 2w = 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 + 2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2w = 0 + -3
2w = 0 + -3

Combine like terms: 0 + -3 = -3
2w = -3

Divide each side by '2'.
w = -1.5

Simplifying
w = -1.5
Solution
w = {-2.2, -1.5}