4w^2-112w+159=0

Solution for 4w^2-112w+159=0 equation:

Simplifying
4w2 + -112w + 159 = 0

Reorder the terms:
159 + -112w + 4w2 = 0

Solving
159 + -112w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(3 + -2w)(53 + -2w) = 0

Subproblem 1
Set the factor '(3 + -2w)' equal to zero and attempt to solve:

Simplifying
3 + -2w = 0

Solving
3 + -2w = 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 + -2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2w = 0 + -3
-2w = 0 + -3

Combine like terms: 0 + -3 = -3
-2w = -3

Divide each side by '-2'.
w = 1.5

Simplifying
w = 1.5
Subproblem 2
Set the factor '(53 + -2w)' equal to zero and attempt to solve:

Simplifying
53 + -2w = 0

Solving
53 + -2w = 0

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

Add '-53' to each side of the equation.
53 + -53 + -2w = 0 + -53

Combine like terms: 53 + -53 = 0
0 + -2w = 0 + -53
-2w = 0 + -53

Combine like terms: 0 + -53 = -53
-2w = -53

Divide each side by '-2'.
w = 26.5

Simplifying
w = 26.5
Solution
w = {1.5, 26.5}