4w^2+33w+54=0

Solution for 4w^2+33w+54=0 equation:

Simplifying
4w2 + 33w + 54 = 0

Reorder the terms:
54 + 33w + 4w2 = 0

Solving
54 + 33w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(6 + w)(9 + 4w) = 0

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 '(9 + 4w)' equal to zero and attempt to solve:

Simplifying
9 + 4w = 0

Solving
9 + 4w = 0

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

Add '-9' to each side of the equation.
9 + -9 + 4w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4w = 0 + -9
4w = 0 + -9

Combine like terms: 0 + -9 = -9
4w = -9

Divide each side by '4'.
w = -2.25

Simplifying
w = -2.25
Solution
w = {-6, -2.25}