(5y+3)(y+6)=-2(5y+3)

Solution for (5y+3)(y+6)=-2(5y+3) equation:

Simplifying
(5y + 3)(y + 6) = -2(5y + 3)

Reorder the terms:
(3 + 5y)(y + 6) = -2(5y + 3)

Reorder the terms:
(3 + 5y)(6 + y) = -2(5y + 3)

Multiply (3 + 5y) * (6 + y)
(3(6 + y) + 5y * (6 + y)) = -2(5y + 3)
((6 * 3 + y * 3) + 5y * (6 + y)) = -2(5y + 3)
((18 + 3y) + 5y * (6 + y)) = -2(5y + 3)
(18 + 3y + (6 * 5y + y * 5y)) = -2(5y + 3)
(18 + 3y + (30y + 5y2)) = -2(5y + 3)

Combine like terms: 3y + 30y = 33y
(18 + 33y + 5y2) = -2(5y + 3)

Reorder the terms:
18 + 33y + 5y2 = -2(3 + 5y)
18 + 33y + 5y2 = (3 * -2 + 5y * -2)
18 + 33y + 5y2 = (-6 + -10y)

Solving
18 + 33y + 5y2 = -6 + -10y

Solving for variable 'y'.

Reorder the terms:
18 + 6 + 33y + 10y + 5y2 = -6 + -10y + 6 + 10y

Combine like terms: 18 + 6 = 24
24 + 33y + 10y + 5y2 = -6 + -10y + 6 + 10y

Combine like terms: 33y + 10y = 43y
24 + 43y + 5y2 = -6 + -10y + 6 + 10y

Reorder the terms:
24 + 43y + 5y2 = -6 + 6 + -10y + 10y

Combine like terms: -6 + 6 = 0
24 + 43y + 5y2 = 0 + -10y + 10y
24 + 43y + 5y2 = -10y + 10y

Combine like terms: -10y + 10y = 0
24 + 43y + 5y2 = 0

Factor a trinomial.
(8 + y)(3 + 5y) = 0

Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve:

Simplifying
8 + y = 0

Solving
8 + y = 0

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

Add '-8' to each side of the equation.
8 + -8 + y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + y = 0 + -8
y = 0 + -8

Combine like terms: 0 + -8 = -8
y = -8

Simplifying
y = -8
Subproblem 2
Set the factor '(3 + 5y)' equal to zero and attempt to solve:

Simplifying
3 + 5y = 0

Solving
3 + 5y = 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 + 5y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5y = 0 + -3
5y = 0 + -3

Combine like terms: 0 + -3 = -3
5y = -3

Divide each side by '5'.
y = -0.6

Simplifying
y = -0.6
Solution
y = {-8, -0.6}