(p-5)(p+3)=

Solution for (p-5)(p+3)= equation:

Simplifying
(p + -5)(p + 3) = 0

Reorder the terms:
(-5 + p)(p + 3) = 0

Reorder the terms:
(-5 + p)(3 + p) = 0

Multiply (-5 + p) * (3 + p)
(-5(3 + p) + p(3 + p)) = 0
((3 * -5 + p * -5) + p(3 + p)) = 0
((-15 + -5p) + p(3 + p)) = 0
(-15 + -5p + (3 * p + p * p)) = 0
(-15 + -5p + (3p + p2)) = 0

Combine like terms: -5p + 3p = -2p
(-15 + -2p + p2) = 0

Solving
-15 + -2p + p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-3 + -1p)(5 + -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 '(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
Solution
p = {-3, 5}