(p+2)(p+3)=p-1

Solution for (p+2)(p+3)=p-1 equation:

Simplifying
(p + 2)(p + 3) = p + -1

Reorder the terms:
(2 + p)(p + 3) = p + -1

Reorder the terms:
(2 + p)(3 + p) = p + -1

Multiply (2 + p) * (3 + p)
(2(3 + p) + p(3 + p)) = p + -1
((3 * 2 + p * 2) + p(3 + p)) = p + -1
((6 + 2p) + p(3 + p)) = p + -1
(6 + 2p + (3 * p + p * p)) = p + -1
(6 + 2p + (3p + p2)) = p + -1

Combine like terms: 2p + 3p = 5p
(6 + 5p + p2) = p + -1

Reorder the terms:
6 + 5p + p2 = -1 + p

Solving
6 + 5p + p2 = -1 + p

Solving for variable 'p'.

Reorder the terms:
6 + 1 + 5p + -1p + p2 = -1 + p + 1 + -1p

Combine like terms: 6 + 1 = 7
7 + 5p + -1p + p2 = -1 + p + 1 + -1p

Combine like terms: 5p + -1p = 4p
7 + 4p + p2 = -1 + p + 1 + -1p

Reorder the terms:
7 + 4p + p2 = -1 + 1 + p + -1p

Combine like terms: -1 + 1 = 0
7 + 4p + p2 = 0 + p + -1p
7 + 4p + p2 = p + -1p

Combine like terms: p + -1p = 0
7 + 4p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 4p + -7 + p2 = 0 + -7

Reorder the terms:
7 + -7 + 4p + p2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4p + p2 = 0 + -7
4p + p2 = 0 + -7

Combine like terms: 0 + -7 = -7
4p + p2 = -7

The p term is 4p.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4p + 4 + p2 = -7 + 4

Reorder the terms:
4 + 4p + p2 = -7 + 4

Combine like terms: -7 + 4 = -3
4 + 4p + p2 = -3

Factor a perfect square on the left side:
(p + 2)(p + 2) = -3

Can't calculate square root of the right side.

The solution to this equation could not be determined.