9w^2+14w+5=0

Solution for 9w^2+14w+5=0 equation:

Simplifying
9w2 + 14w + 5 = 0

Reorder the terms:
5 + 14w + 9w2 = 0

Solving
5 + 14w + 9w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(1 + w)(5 + 9w) = 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 '(5 + 9w)' equal to zero and attempt to solve:

Simplifying
5 + 9w = 0

Solving
5 + 9w = 0

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

Add '-5' to each side of the equation.
5 + -5 + 9w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 9w = 0 + -5
9w = 0 + -5

Combine like terms: 0 + -5 = -5
9w = -5

Divide each side by '9'.
w = -0.5555555556

Simplifying
w = -0.5555555556
Solution
w = {-1, -0.5555555556}