p^2-10p-75=0

Solution for p^2-10p-75=0 equation:

Simplifying
p2 + -10p + -75 = 0

Reorder the terms:
-75 + -10p + p2 = 0

Solving
-75 + -10p + p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-5 + -1p)(15 + -1p) = 0

Subproblem 1
Set the factor '(-5 + -1p)' equal to zero and attempt to solve:

Simplifying
-5 + -1p = 0

Solving
-5 + -1p = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1p = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1p = 0 + 5
-1p = 0 + 5

Combine like terms: 0 + 5 = 5
-1p = 5

Divide each side by '-1'.
p = -5

Simplifying
p = -5
Subproblem 2
Set the factor '(15 + -1p)' equal to zero and attempt to solve:

Simplifying
15 + -1p = 0

Solving
15 + -1p = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1p = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1p = 0 + -15
-1p = 0 + -15

Combine like terms: 0 + -15 = -15
-1p = -15

Divide each side by '-1'.
p = 15

Simplifying
p = 15
Solution
p = {-5, 15}