(y+3)(y+4)=2

Solution for (y+3)(y+4)=2 equation:

Simplifying
(y + 3)(y + 4) = 2

Reorder the terms:
(3 + y)(y + 4) = 2

Reorder the terms:
(3 + y)(4 + y) = 2

Multiply (3 + y) * (4 + y)
(3(4 + y) + y(4 + y)) = 2
((4 * 3 + y * 3) + y(4 + y)) = 2
((12 + 3y) + y(4 + y)) = 2
(12 + 3y + (4 * y + y * y)) = 2
(12 + 3y + (4y + y2)) = 2

Combine like terms: 3y + 4y = 7y
(12 + 7y + y2) = 2

Solving
12 + 7y + y2 = 2

Solving for variable 'y'.

Reorder the terms:
12 + -2 + 7y + y2 = 2 + -2

Combine like terms: 12 + -2 = 10
10 + 7y + y2 = 2 + -2

Combine like terms: 2 + -2 = 0
10 + 7y + y2 = 0

Factor a trinomial.
(5 + y)(2 + 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 '(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 = {-5, -2}