(p+5)(p-3)=20

Solution for (p+5)(p-3)=20 equation:

Simplifying
(p + 5)(p + -3) = 20

Reorder the terms:
(5 + p)(p + -3) = 20

Reorder the terms:
(5 + p)(-3 + p) = 20

Multiply (5 + p) * (-3 + p)
(5(-3 + p) + p(-3 + p)) = 20
((-3 * 5 + p * 5) + p(-3 + p)) = 20
((-15 + 5p) + p(-3 + p)) = 20
(-15 + 5p + (-3 * p + p * p)) = 20
(-15 + 5p + (-3p + p2)) = 20

Combine like terms: 5p + -3p = 2p
(-15 + 2p + p2) = 20

Solving
-15 + 2p + p2 = 20

Solving for variable 'p'.

Reorder the terms:
-15 + -20 + 2p + p2 = 20 + -20

Combine like terms: -15 + -20 = -35
-35 + 2p + p2 = 20 + -20

Combine like terms: 20 + -20 = 0
-35 + 2p + p2 = 0

Factor a trinomial.
(-7 + -1p)(5 + -1p) = 0

Subproblem 1
Set the factor '(-7 + -1p)' equal to zero and attempt to solve:

Simplifying
-7 + -1p = 0

Solving
-7 + -1p = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1p = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1p = 0 + 7
-1p = 0 + 7

Combine like terms: 0 + 7 = 7
-1p = 7

Divide each side by '-1'.
p = -7

Simplifying
p = -7
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 = {-7, 5}