5w^2+9w+4=0

Solution for 5w^2+9w+4=0 equation:

Simplifying
5w2 + 9w + 4 = 0

Reorder the terms:
4 + 9w + 5w2 = 0

Solving
4 + 9w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(1 + w)(4 + 5w) = 0

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

Simplifying
1 + w = 0

Solving
1 + w = 0

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

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

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

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

Simplifying
w = -1
Subproblem 2
Set the factor '(4 + 5w)' equal to zero and attempt to solve:

Simplifying
4 + 5w = 0

Solving
4 + 5w = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5w = 0 + -4
5w = 0 + -4

Combine like terms: 0 + -4 = -4
5w = -4

Divide each side by '5'.
w = -0.8

Simplifying
w = -0.8
Solution
w = {-1, -0.8}