(p+1)(p-5)=2(p+1)

Solution for (p+1)(p-5)=2(p+1) equation:

Simplifying
(p + 1)(p + -5) = 2(p + 1)

Reorder the terms:
(1 + p)(p + -5) = 2(p + 1)

Reorder the terms:
(1 + p)(-5 + p) = 2(p + 1)

Multiply (1 + p) * (-5 + p)
(1(-5 + p) + p(-5 + p)) = 2(p + 1)
((-5 * 1 + p * 1) + p(-5 + p)) = 2(p + 1)
((-5 + 1p) + p(-5 + p)) = 2(p + 1)
(-5 + 1p + (-5 * p + p * p)) = 2(p + 1)
(-5 + 1p + (-5p + p2)) = 2(p + 1)

Combine like terms: 1p + -5p = -4p
(-5 + -4p + p2) = 2(p + 1)

Reorder the terms:
-5 + -4p + p2 = 2(1 + p)
-5 + -4p + p2 = (1 * 2 + p * 2)
-5 + -4p + p2 = (2 + 2p)

Solving
-5 + -4p + p2 = 2 + 2p

Solving for variable 'p'.

Reorder the terms:
-5 + -2 + -4p + -2p + p2 = 2 + 2p + -2 + -2p

Combine like terms: -5 + -2 = -7
-7 + -4p + -2p + p2 = 2 + 2p + -2 + -2p

Combine like terms: -4p + -2p = -6p
-7 + -6p + p2 = 2 + 2p + -2 + -2p

Reorder the terms:
-7 + -6p + p2 = 2 + -2 + 2p + -2p

Combine like terms: 2 + -2 = 0
-7 + -6p + p2 = 0 + 2p + -2p
-7 + -6p + p2 = 2p + -2p

Combine like terms: 2p + -2p = 0
-7 + -6p + p2 = 0

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

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

Simplifying
-1 + -1p = 0

Solving
-1 + -1p = 0

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

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

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

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

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

Simplifying
p = -1
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 = {-1, 7}