0=13p-p^2-30

Solution for 0=13p-p^2-30 equation:

Simplifying
0 = 13p + -1p2 + -30

Reorder the terms:
0 = -30 + 13p + -1p2

Solving
0 = -30 + 13p + -1p2

Solving for variable 'p'.

Combine like terms: 0 + 30 = 30
30 + -13p + p2 = -30 + 13p + -1p2 + 30 + -13p + p2

Reorder the terms:
30 + -13p + p2 = -30 + 30 + 13p + -13p + -1p2 + p2

Combine like terms: -30 + 30 = 0
30 + -13p + p2 = 0 + 13p + -13p + -1p2 + p2
30 + -13p + p2 = 13p + -13p + -1p2 + p2

Combine like terms: 13p + -13p = 0
30 + -13p + p2 = 0 + -1p2 + p2
30 + -13p + p2 = -1p2 + p2

Combine like terms: -1p2 + p2 = 0
30 + -13p + p2 = 0

Factor a trinomial.
(3 + -1p)(10 + -1p) = 0

Subproblem 1
Set the factor '(3 + -1p)' equal to zero and attempt to solve:

Simplifying
3 + -1p = 0

Solving
3 + -1p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Subproblem 2
Set the factor '(10 + -1p)' equal to zero and attempt to solve:

Simplifying
10 + -1p = 0

Solving
10 + -1p = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1p = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1p = 0 + -10
-1p = 0 + -10

Combine like terms: 0 + -10 = -10
-1p = -10

Divide each side by '-1'.
p = 10

Simplifying
p = 10
Solution
p = {3, 10}