4w^2-19w-5=0

Solution for 4w^2-19w-5=0 equation:

Simplifying
4w2 + -19w + -5 = 0

Reorder the terms:
-5 + -19w + 4w2 = 0

Solving
-5 + -19w + 4w2 = 0

Solving for variable 'w'.

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

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

Simplifying
-1 + -4w = 0

Solving
-1 + -4w = 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 + -4w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4w = 0 + 1
-4w = 0 + 1

Combine like terms: 0 + 1 = 1
-4w = 1

Divide each side by '-4'.
w = -0.25

Simplifying
w = -0.25
Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 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 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {-0.25, 5}