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

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

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

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

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

Multiply (3 + 4y) * (5 + y)
(3(5 + y) + 4y * (5 + y)) = -2(4y + 3)
((5 * 3 + y * 3) + 4y * (5 + y)) = -2(4y + 3)
((15 + 3y) + 4y * (5 + y)) = -2(4y + 3)
(15 + 3y + (5 * 4y + y * 4y)) = -2(4y + 3)
(15 + 3y + (20y + 4y2)) = -2(4y + 3)

Combine like terms: 3y + 20y = 23y
(15 + 23y + 4y2) = -2(4y + 3)

Reorder the terms:
15 + 23y + 4y2 = -2(3 + 4y)
15 + 23y + 4y2 = (3 * -2 + 4y * -2)
15 + 23y + 4y2 = (-6 + -8y)

Solving
15 + 23y + 4y2 = -6 + -8y

Solving for variable 'y'.

Reorder the terms:
15 + 6 + 23y + 8y + 4y2 = -6 + -8y + 6 + 8y

Combine like terms: 15 + 6 = 21
21 + 23y + 8y + 4y2 = -6 + -8y + 6 + 8y

Combine like terms: 23y + 8y = 31y
21 + 31y + 4y2 = -6 + -8y + 6 + 8y

Reorder the terms:
21 + 31y + 4y2 = -6 + 6 + -8y + 8y

Combine like terms: -6 + 6 = 0
21 + 31y + 4y2 = 0 + -8y + 8y
21 + 31y + 4y2 = -8y + 8y

Combine like terms: -8y + 8y = 0
21 + 31y + 4y2 = 0

Factor a trinomial.
(7 + y)(3 + 4y) = 0

Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

Solving
7 + y = 0

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

Add '-7' to each side of the equation.
7 + -7 + y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + y = 0 + -7
y = 0 + -7

Combine like terms: 0 + -7 = -7
y = -7

Simplifying
y = -7
Subproblem 2
Set the factor '(3 + 4y)' equal to zero and attempt to solve:

Simplifying
3 + 4y = 0

Solving
3 + 4y = 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 + 4y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4y = 0 + -3
4y = 0 + -3

Combine like terms: 0 + -3 = -3
4y = -3

Divide each side by '4'.
y = -0.75

Simplifying
y = -0.75
Solution
y = {-7, -0.75}