(y+2)(y+3)=-y+1

Solution for (y+2)(y+3)=-y+1 equation:

Simplifying
(y + 2)(y + 3) = -1y + 1

Reorder the terms:
(2 + y)(y + 3) = -1y + 1

Reorder the terms:
(2 + y)(3 + y) = -1y + 1

Multiply (2 + y) * (3 + y)
(2(3 + y) + y(3 + y)) = -1y + 1
((3 * 2 + y * 2) + y(3 + y)) = -1y + 1
((6 + 2y) + y(3 + y)) = -1y + 1
(6 + 2y + (3 * y + y * y)) = -1y + 1
(6 + 2y + (3y + y2)) = -1y + 1

Combine like terms: 2y + 3y = 5y
(6 + 5y + y2) = -1y + 1

Reorder the terms:
6 + 5y + y2 = 1 + -1y

Solving
6 + 5y + y2 = 1 + -1y

Solving for variable 'y'.

Reorder the terms:
6 + -1 + 5y + y + y2 = 1 + -1y + -1 + y

Combine like terms: 6 + -1 = 5
5 + 5y + y + y2 = 1 + -1y + -1 + y

Combine like terms: 5y + y = 6y
5 + 6y + y2 = 1 + -1y + -1 + y

Reorder the terms:
5 + 6y + y2 = 1 + -1 + -1y + y

Combine like terms: 1 + -1 = 0
5 + 6y + y2 = 0 + -1y + y
5 + 6y + y2 = -1y + y

Combine like terms: -1y + y = 0
5 + 6y + y2 = 0

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

Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + y = 0 + -5
y = 0 + -5

Combine like terms: 0 + -5 = -5
y = -5

Simplifying
y = -5
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 = {-5, -1}