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

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

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

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

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

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

Combine like terms: 4y + 3y = 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}