(y+3)(2y+3)=5

Solution for (y+3)(2y+3)=5 equation:

Simplifying
(y + 3)(2y + 3) = 5

Reorder the terms:
(3 + y)(2y + 3) = 5

Reorder the terms:
(3 + y)(3 + 2y) = 5

Multiply (3 + y) * (3 + 2y)
(3(3 + 2y) + y(3 + 2y)) = 5
((3 * 3 + 2y * 3) + y(3 + 2y)) = 5
((9 + 6y) + y(3 + 2y)) = 5
(9 + 6y + (3 * y + 2y * y)) = 5
(9 + 6y + (3y + 2y2)) = 5

Combine like terms: 6y + 3y = 9y
(9 + 9y + 2y2) = 5

Solving
9 + 9y + 2y2 = 5

Solving for variable 'y'.

Reorder the terms:
9 + -5 + 9y + 2y2 = 5 + -5

Combine like terms: 9 + -5 = 4
4 + 9y + 2y2 = 5 + -5

Combine like terms: 5 + -5 = 0
4 + 9y + 2y2 = 0

Factor a trinomial.
(4 + y)(1 + 2y) = 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 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 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 + 2y = 0 + -1

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

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

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {-4, -0.5}