(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 = 8p
(15 + 8p + p2) = 2(p + 3)

Reorder the terms:
15 + 8p + p2 = 2(3 + p)
15 + 8p + p2 = (3 * 2 + p * 2)
15 + 8p + p2 = (6 + 2p)

Solving
15 + 8p + p2 = 6 + 2p

Solving for variable 'p'.

Reorder the terms:
15 + -6 + 8p + -2p + p2 = 6 + 2p + -6 + -2p

Combine like terms: 15 + -6 = 9
9 + 8p + -2p + p2 = 6 + 2p + -6 + -2p

Combine like terms: 8p + -2p = 6p
9 + 6p + p2 = 6 + 2p + -6 + -2p

Reorder the terms:
9 + 6p + p2 = 6 + -6 + 2p + -2p

Combine like terms: 6 + -6 = 0
9 + 6p + p2 = 0 + 2p + -2p
9 + 6p + p2 = 2p + -2p

Combine like terms: 2p + -2p = 0
9 + 6p + p2 = 0

Factor a trinomial.
(3 + p)(3 + p) = 0

Subproblem 1
Set the factor '(3 + p)' equal to zero and attempt to solve:

Simplifying
3 + p = 0

Solving
3 + p = 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 + p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + p = 0 + -3
p = 0 + -3

Combine like terms: 0 + -3 = -3
p = -3

Simplifying
p = -3
Subproblem 2
Set the factor '(3 + p)' equal to zero and attempt to solve:

Simplifying
3 + p = 0

Solving
3 + p = 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 + p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + p = 0 + -3
p = 0 + -3

Combine like terms: 0 + -3 = -3
p = -3

Simplifying
p = -3
Solution
p = {-3, -3}