-w^2+19w-60=0

Solution for -w^2+19w-60=0 equation:

Simplifying
-1w2 + 19w + -60 = 0

Reorder the terms:
-60 + 19w + -1w2 = 0

Solving
-60 + 19w + -1w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-15 + w)(4 + -1w) = 0

Subproblem 1
Set the factor '(-15 + w)' equal to zero and attempt to solve:

Simplifying
-15 + w = 0

Solving
-15 + w = 0

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

Add '15' to each side of the equation.
-15 + 15 + w = 0 + 15

Combine like terms: -15 + 15 = 0
0 + w = 0 + 15
w = 0 + 15

Combine like terms: 0 + 15 = 15
w = 15

Simplifying
w = 15
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 = {15, 4}