4w^2+19w+12=0

Solution for 4w^2+19w+12=0 equation:

Simplifying
4w2 + 19w + 12 = 0

Reorder the terms:
12 + 19w + 4w2 = 0

Solving
12 + 19w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(4 + w)(3 + 4w) = 0

Subproblem 1
Set the factor '(4 + w)' equal to zero and attempt to solve:

Simplifying
4 + w = 0

Solving
4 + w = 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 + w = 0 + -4

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

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

Simplifying
w = -4
Subproblem 2
Set the factor '(3 + 4w)' equal to zero and attempt to solve:

Simplifying
3 + 4w = 0

Solving
3 + 4w = 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 + 4w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4w = 0 + -3
4w = 0 + -3

Combine like terms: 0 + -3 = -3
4w = -3

Divide each side by '4'.
w = -0.75

Simplifying
w = -0.75
Solution
w = {-4, -0.75}