p^2-4p-32=13

Solution for p^2-4p-32=13 equation:

Simplifying
p2 + -4p + -32 = 13

Reorder the terms:
-32 + -4p + p2 = 13

Solving
-32 + -4p + p2 = 13

Solving for variable 'p'.

Reorder the terms:
-32 + -13 + -4p + p2 = 13 + -13

Combine like terms: -32 + -13 = -45
-45 + -4p + p2 = 13 + -13

Combine like terms: 13 + -13 = 0
-45 + -4p + p2 = 0

Factor a trinomial.
(-5 + -1p)(9 + -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 '(9 + -1p)' equal to zero and attempt to solve:

Simplifying
9 + -1p = 0

Solving
9 + -1p = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1p = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1p = 0 + -9
-1p = 0 + -9

Combine like terms: 0 + -9 = -9
-1p = -9

Divide each side by '-1'.
p = 9

Simplifying
p = 9
Solution
p = {-5, 9}