(2y+3)(y+5)=-4(2y+3)

Solution for (2y+3)(y+5)=-4(2y+3) equation:

Simplifying
(2y + 3)(y + 5) = -4(2y + 3)

Reorder the terms:
(3 + 2y)(y + 5) = -4(2y + 3)

Reorder the terms:
(3 + 2y)(5 + y) = -4(2y + 3)

Multiply (3 + 2y) * (5 + y)
(3(5 + y) + 2y * (5 + y)) = -4(2y + 3)
((5 * 3 + y * 3) + 2y * (5 + y)) = -4(2y + 3)
((15 + 3y) + 2y * (5 + y)) = -4(2y + 3)
(15 + 3y + (5 * 2y + y * 2y)) = -4(2y + 3)
(15 + 3y + (10y + 2y2)) = -4(2y + 3)

Combine like terms: 3y + 10y = 13y
(15 + 13y + 2y2) = -4(2y + 3)

Reorder the terms:
15 + 13y + 2y2 = -4(3 + 2y)
15 + 13y + 2y2 = (3 * -4 + 2y * -4)
15 + 13y + 2y2 = (-12 + -8y)

Solving
15 + 13y + 2y2 = -12 + -8y

Solving for variable 'y'.

Reorder the terms:
15 + 12 + 13y + 8y + 2y2 = -12 + -8y + 12 + 8y

Combine like terms: 15 + 12 = 27
27 + 13y + 8y + 2y2 = -12 + -8y + 12 + 8y

Combine like terms: 13y + 8y = 21y
27 + 21y + 2y2 = -12 + -8y + 12 + 8y

Reorder the terms:
27 + 21y + 2y2 = -12 + 12 + -8y + 8y

Combine like terms: -12 + 12 = 0
27 + 21y + 2y2 = 0 + -8y + 8y
27 + 21y + 2y2 = -8y + 8y

Combine like terms: -8y + 8y = 0
27 + 21y + 2y2 = 0

Factor a trinomial.
(9 + y)(3 + 2y) = 0

Subproblem 1
Set the factor '(9 + y)' equal to zero and attempt to solve:

Simplifying
9 + y = 0

Solving
9 + y = 0

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

Add '-9' to each side of the equation.
9 + -9 + y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + y = 0 + -9
y = 0 + -9

Combine like terms: 0 + -9 = -9
y = -9

Simplifying
y = -9
Subproblem 2
Set the factor '(3 + 2y)' equal to zero and attempt to solve:

Simplifying
3 + 2y = 0

Solving
3 + 2y = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2y = 0 + -3
2y = 0 + -3

Combine like terms: 0 + -3 = -3
2y = -3

Divide each side by '2'.
y = -1.5

Simplifying
y = -1.5
Solution
y = {-9, -1.5}