F(w)=-w^2+60w

Solution for F(w)=-w^2+60w equation:

Simplifying
F(w) = -1w2 + 60w

Multiply F * w
wF = -1w2 + 60w

Reorder the terms:
wF = 60w + -1w2

Solving
wF = 60w + -1w2

Solving for variable 'w'.

Reorder the terms:
-60w + wF + w2 = 60w + -1w2 + -60w + w2

Reorder the terms:
-60w + wF + w2 = 60w + -60w + -1w2 + w2

Combine like terms: 60w + -60w = 0
-60w + wF + w2 = 0 + -1w2 + w2
-60w + wF + w2 = -1w2 + w2

Combine like terms: -1w2 + w2 = 0
-60w + wF + w2 = 0

Factor out the Greatest Common Factor (GCF), 'w'.
w(-60 + F + w) = 0

Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0
Subproblem 2
Set the factor '(-60 + F + w)' equal to zero and attempt to solve:

Simplifying
-60 + F + w = 0

Solving
-60 + F + w = 0

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

Add '60' to each side of the equation.
-60 + F + 60 + w = 0 + 60

Reorder the terms:
-60 + 60 + F + w = 0 + 60

Combine like terms: -60 + 60 = 0
0 + F + w = 0 + 60
F + w = 0 + 60

Combine like terms: 0 + 60 = 60
F + w = 60

Add '-1F' to each side of the equation.
F + -1F + w = 60 + -1F

Combine like terms: F + -1F = 0
0 + w = 60 + -1F
w = 60 + -1F

Simplifying
w = 60 + -1F
Solution
w = {0, 60 + -1F}