T(p)=60p-p^2

Solution for T(p)=60p-p^2 equation:

Simplifying
T(p) = 60p + -1p2

Multiply T * p
pT = 60p + -1p2

Solving
pT = 60p + -1p2

Solving for variable 'p'.

Reorder the terms:
-60p + pT + p2 = 60p + -1p2 + -60p + p2

Reorder the terms:
-60p + pT + p2 = 60p + -60p + -1p2 + p2

Combine like terms: 60p + -60p = 0
-60p + pT + p2 = 0 + -1p2 + p2
-60p + pT + p2 = -1p2 + p2

Combine like terms: -1p2 + p2 = 0
-60p + pT + p2 = 0

Factor out the Greatest Common Factor (GCF), 'p'.
p(-60 + T + p) = 0

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

Simplifying
p = 0

Solving
p = 0

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

Simplifying
p = 0
Subproblem 2
Set the factor '(-60 + T + p)' equal to zero and attempt to solve:

Simplifying
-60 + T + p = 0

Solving
-60 + T + p = 0

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

Add '60' to each side of the equation.
-60 + T + 60 + p = 0 + 60

Reorder the terms:
-60 + 60 + T + p = 0 + 60

Combine like terms: -60 + 60 = 0
0 + T + p = 0 + 60
T + p = 0 + 60

Combine like terms: 0 + 60 = 60
T + p = 60

Add '-1T' to each side of the equation.
T + -1T + p = 60 + -1T

Combine like terms: T + -1T = 0
0 + p = 60 + -1T
p = 60 + -1T

Simplifying
p = 60 + -1T
Solution
p = {0, 60 + -1T}