4w^2-11w-20=0

Solution for 4w^2-11w-20=0 equation:

Simplifying
4w2 + -11w + -20 = 0

Reorder the terms:
-20 + -11w + 4w2 = 0

Solving
-20 + -11w + 4w2 = 0

Solving for variable 'w'.

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

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

Simplifying
-5 + -4w = 0

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

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

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

Divide each side by '-4'.
w = -1.25

Simplifying
w = -1.25
Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

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

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

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

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {-1.25, 4}