3w^2+19w+16=0

Solution for 3w^2+19w+16=0 equation:

Simplifying
3w2 + 19w + 16 = 0

Reorder the terms:
16 + 19w + 3w2 = 0

Solving
16 + 19w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(16 + 3w)(1 + w) = 0

Subproblem 1
Set the factor '(16 + 3w)' equal to zero and attempt to solve:

Simplifying
16 + 3w = 0

Solving
16 + 3w = 0

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

Add '-16' to each side of the equation.
16 + -16 + 3w = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 3w = 0 + -16
3w = 0 + -16

Combine like terms: 0 + -16 = -16
3w = -16

Divide each side by '3'.
w = -5.333333333

Simplifying
w = -5.333333333
Subproblem 2
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
Solution
w = {-5.333333333, -1}