p^2=-2p-1

Solution for p^2=-2p-1 equation:

Simplifying
p2 = -2p + -1

Reorder the terms:
p2 = -1 + -2p

Solving
p2 = -1 + -2p

Solving for variable 'p'.

Reorder the terms:
1 + 2p + p2 = -1 + -2p + 1 + 2p

Reorder the terms:
1 + 2p + p2 = -1 + 1 + -2p + 2p

Combine like terms: -1 + 1 = 0
1 + 2p + p2 = 0 + -2p + 2p
1 + 2p + p2 = -2p + 2p

Combine like terms: -2p + 2p = 0
1 + 2p + p2 = 0

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

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

Simplifying
1 + p = 0

Solving
1 + p = 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 + p = 0 + -1

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

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

Simplifying
p = -1
Subproblem 2
Set the factor '(1 + p)' equal to zero and attempt to solve:

Simplifying
1 + p = 0

Solving
1 + p = 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 + p = 0 + -1

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

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

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