e^2+2e+1=0

Solution for e^2+2e+1=0 equation:

Simplifying
e2 + 2e + 1 = 0

Reorder the terms:
1 + 2e + e2 = 0

Solving
1 + 2e + e2 = 0

Solving for variable 'e'.

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

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

Simplifying
1 + e = 0

Solving
1 + e = 0

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

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

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

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

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

Simplifying
1 + e = 0

Solving
1 + e = 0

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

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

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

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

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