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

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

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

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

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

Multiply (3 + 2y) * (4 + y)
(3(4 + y) + 2y * (4 + y)) = -2(2y + 3)
((4 * 3 + y * 3) + 2y * (4 + y)) = -2(2y + 3)
((12 + 3y) + 2y * (4 + y)) = -2(2y + 3)
(12 + 3y + (4 * 2y + y * 2y)) = -2(2y + 3)
(12 + 3y + (8y + 2y2)) = -2(2y + 3)

Combine like terms: 3y + 8y = 11y
(12 + 11y + 2y2) = -2(2y + 3)

Reorder the terms:
12 + 11y + 2y2 = -2(3 + 2y)
12 + 11y + 2y2 = (3 * -2 + 2y * -2)
12 + 11y + 2y2 = (-6 + -4y)

Solving
12 + 11y + 2y2 = -6 + -4y

Solving for variable 'y'.

Reorder the terms:
12 + 6 + 11y + 4y + 2y2 = -6 + -4y + 6 + 4y

Combine like terms: 12 + 6 = 18
18 + 11y + 4y + 2y2 = -6 + -4y + 6 + 4y

Combine like terms: 11y + 4y = 15y
18 + 15y + 2y2 = -6 + -4y + 6 + 4y

Reorder the terms:
18 + 15y + 2y2 = -6 + 6 + -4y + 4y

Combine like terms: -6 + 6 = 0
18 + 15y + 2y2 = 0 + -4y + 4y
18 + 15y + 2y2 = -4y + 4y

Combine like terms: -4y + 4y = 0
18 + 15y + 2y2 = 0

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

Subproblem 1
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6
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 = {-6, -1.5}