3w^2+2w=33

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

Simplifying
3w2 + 2w = 33

Reorder the terms:
2w + 3w2 = 33

Solving
2w + 3w2 = 33

Solving for variable 'w'.

Reorder the terms:
-33 + 2w + 3w2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + 2w + 3w2 = 0

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

Subproblem 1
Set the factor '(-11 + -3w)' equal to zero and attempt to solve:

Simplifying
-11 + -3w = 0

Solving
-11 + -3w = 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 + -3w = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3w = 0 + 11
-3w = 0 + 11

Combine like terms: 0 + 11 = 11
-3w = 11

Divide each side by '-3'.
w = -3.666666667

Simplifying
w = -3.666666667
Subproblem 2
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
Solution
w = {-3.666666667, 3}