9(p)=60p-p^2

Solution for 9(p)=60p-p^2 equation:

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

Solving
9p = 60p + -1p2

Solving for variable 'p'.

Combine like terms: 9p + -60p = -51p
-51p + p2 = 60p + -1p2 + -60p + p2

Reorder the terms:
-51p + p2 = 60p + -60p + -1p2 + p2

Combine like terms: 60p + -60p = 0
-51p + p2 = 0 + -1p2 + p2
-51p + p2 = -1p2 + p2

Combine like terms: -1p2 + p2 = 0
-51p + p2 = 0

Factor out the Greatest Common Factor (GCF), 'p'.
p(-51 + 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 '(-51 + p)' equal to zero and attempt to solve:

Simplifying
-51 + p = 0

Solving
-51 + p = 0

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

Add '51' to each side of the equation.
-51 + 51 + p = 0 + 51

Combine like terms: -51 + 51 = 0
0 + p = 0 + 51
p = 0 + 51

Combine like terms: 0 + 51 = 51
p = 51

Simplifying
p = 51
Solution
p = {0, 51}