(p+3)(p-5)=2(p+3)

Solution for (p+3)(p-5)=2(p+3) equation:

Simplifying
(p + 3)(p + -5) = 2(p + 3)

Reorder the terms:
(3 + p)(p + -5) = 2(p + 3)

Reorder the terms:
(3 + p)(-5 + p) = 2(p + 3)

Multiply (3 + p) * (-5 + p)
(3(-5 + p) + p(-5 + p)) = 2(p + 3)
((-5 * 3 + p * 3) + p(-5 + p)) = 2(p + 3)
((-15 + 3p) + p(-5 + p)) = 2(p + 3)
(-15 + 3p + (-5 * p + p * p)) = 2(p + 3)
(-15 + 3p + (-5p + p2)) = 2(p + 3)

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

Reorder the terms:
-15 + -2p + p2 = 2(3 + p)
-15 + -2p + p2 = (3 * 2 + p * 2)
-15 + -2p + p2 = (6 + 2p)

Solving
-15 + -2p + p2 = 6 + 2p

Solving for variable 'p'.

Reorder the terms:
-15 + -6 + -2p + -2p + p2 = 6 + 2p + -6 + -2p

Combine like terms: -15 + -6 = -21
-21 + -2p + -2p + p2 = 6 + 2p + -6 + -2p

Combine like terms: -2p + -2p = -4p
-21 + -4p + p2 = 6 + 2p + -6 + -2p

Reorder the terms:
-21 + -4p + p2 = 6 + -6 + 2p + -2p

Combine like terms: 6 + -6 = 0
-21 + -4p + p2 = 0 + 2p + -2p
-21 + -4p + p2 = 2p + -2p

Combine like terms: 2p + -2p = 0
-21 + -4p + p2 = 0

Factor a trinomial.
(-3 + -1p)(7 + -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 '(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
Solution
p = {-3, 7}