(p-3)(p+5)=

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

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

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

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

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

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

Solving
-15 + 2p + p2 = 0

Solving for variable 'p'.

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