y^2+4y+5=-y+1

Solution for y^2+4y+5=-y+1 equation:

Simplifying
y2 + 4y + 5 = -1y + 1

Reorder the terms:
5 + 4y + y2 = -1y + 1

Reorder the terms:
5 + 4y + y2 = 1 + -1y

Solving
5 + 4y + y2 = 1 + -1y

Solving for variable 'y'.

Reorder the terms:
5 + -1 + 4y + y + y2 = 1 + -1y + -1 + y

Combine like terms: 5 + -1 = 4
4 + 4y + y + y2 = 1 + -1y + -1 + y

Combine like terms: 4y + y = 5y
4 + 5y + y2 = 1 + -1y + -1 + y

Reorder the terms:
4 + 5y + y2 = 1 + -1 + -1y + y

Combine like terms: 1 + -1 = 0
4 + 5y + y2 = 0 + -1y + y
4 + 5y + y2 = -1y + y

Combine like terms: -1y + y = 0
4 + 5y + y2 = 0

Factor a trinomial.
(4 + y)(1 + y) = 0

Subproblem 1
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 0

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

Add '-4' to each side of the equation.
4 + -4 + y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + y = 0 + -4
y = 0 + -4

Combine like terms: 0 + -4 = -4
y = -4

Simplifying
y = -4
Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

Simplifying
y = -1
Solution
y = {-4, -1}