p^2+4p+5=1

Solution for p^2+4p+5=1 equation:

Simplifying
p2 + 4p + 5 = 1

Reorder the terms:
5 + 4p + p2 = 1

Solving
5 + 4p + p2 = 1

Solving for variable 'p'.

Reorder the terms:
5 + -1 + 4p + p2 = 1 + -1

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

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

Factor a trinomial.
(2 + p)(2 + p) = 0

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

Simplifying
2 + p = 0

Solving
2 + p = 0

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

Add '-2' to each side of the equation.
2 + -2 + p = 0 + -2

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

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

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

Simplifying
2 + p = 0

Solving
2 + p = 0

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

Add '-2' to each side of the equation.
2 + -2 + p = 0 + -2

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

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

Simplifying
p = -2
Solution
p = {-2, -2}