-w^2+17w-60=0

Solution for -w^2+17w-60=0 equation:

Simplifying
-1w2 + 17w + -60 = 0

Reorder the terms:
-60 + 17w + -1w2 = 0

Solving
-60 + 17w + -1w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-12 + w)(5 + -1w) = 0

Subproblem 1
Set the factor '(-12 + w)' equal to zero and attempt to solve:

Simplifying
-12 + w = 0

Solving
-12 + w = 0

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

Add '12' to each side of the equation.
-12 + 12 + w = 0 + 12

Combine like terms: -12 + 12 = 0
0 + w = 0 + 12
w = 0 + 12

Combine like terms: 0 + 12 = 12
w = 12

Simplifying
w = 12
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 = {12, 5}