y^2+2y+1=1

Solution for y^2+2y+1=1 equation:

Simplifying
y2 + 2y + 1 = 1

Reorder the terms:
1 + 2y + y2 = 1

Add '-1' to each side of the equation.
1 + 2y + -1 + y2 = 1 + -1

Reorder the terms:
1 + -1 + 2y + y2 = 1 + -1

Combine like terms: 1 + -1 = 0
0 + 2y + y2 = 1 + -1
2y + y2 = 1 + -1

Combine like terms: 1 + -1 = 0
2y + y2 = 0

Solving
2y + y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(2 + y) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

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

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

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

Simplifying
y = -2
Solution
y = {0, -2}