4w^2-17w+15=0

Solution for 4w^2-17w+15=0 equation:

Simplifying
4w2 + -17w + 15 = 0

Reorder the terms:
15 + -17w + 4w2 = 0

Solving
15 + -17w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(5 + -4w)(3 + -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 '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 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 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {1.25, 3}