p^2-22p-75=0

Solution for p^2-22p-75=0 equation:

Simplifying
p2 + -22p + -75 = 0

Reorder the terms:
-75 + -22p + p2 = 0

Solving
-75 + -22p + p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-3 + -1p)(25 + -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 '(25 + -1p)' equal to zero and attempt to solve:

Simplifying
25 + -1p = 0

Solving
25 + -1p = 0

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

Add '-25' to each side of the equation.
25 + -25 + -1p = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1p = 0 + -25
-1p = 0 + -25

Combine like terms: 0 + -25 = -25
-1p = -25

Divide each side by '-1'.
p = 25

Simplifying
p = 25
Solution
p = {-3, 25}