(3y+4)(y+6)=-2(3y+4)

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Solution for (3y+4)(y+6)=-2(3y+4) equation: 


Simplifying
(3y + 4)(y + 6) = -2(3y + 4)

Reorder the terms:
(4 + 3y)(y + 6) = -2(3y + 4)

Reorder the terms:
(4 + 3y)(6 + y) = -2(3y + 4)

Multiply (4 + 3y) * (6 + y)
(4(6 + y) + 3y * (6 + y)) = -2(3y + 4)
((6 * 4 + y * 4) + 3y * (6 + y)) = -2(3y + 4)
((24 + 4y) + 3y * (6 + y)) = -2(3y + 4)
(24 + 4y + (6 * 3y + y * 3y)) = -2(3y + 4)
(24 + 4y + (18y + 3y2)) = -2(3y + 4)

Combine like terms: 4y + 18y = 22y
(24 + 22y + 3y2) = -2(3y + 4)

Reorder the terms:
24 + 22y + 3y2 = -2(4 + 3y)
24 + 22y + 3y2 = (4 * -2 + 3y * -2)
24 + 22y + 3y2 = (-8 + -6y)

Solving
24 + 22y + 3y2 = -8 + -6y

Solving for variable 'y'.

Reorder the terms:
24 + 8 + 22y + 6y + 3y2 = -8 + -6y + 8 + 6y

Combine like terms: 24 + 8 = 32
32 + 22y + 6y + 3y2 = -8 + -6y + 8 + 6y

Combine like terms: 22y + 6y = 28y
32 + 28y + 3y2 = -8 + -6y + 8 + 6y

Reorder the terms:
32 + 28y + 3y2 = -8 + 8 + -6y + 6y

Combine like terms: -8 + 8 = 0
32 + 28y + 3y2 = 0 + -6y + 6y
32 + 28y + 3y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
32 + 28y + 3y2 = 0

Factor a trinomial.
(8 + y)(4 + 3y) = 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 '(4 + 3y)' equal to zero and attempt to solve:

Simplifying
4 + 3y = 0

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

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

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

Divide each side by '3'.
y = -1.333333333

Simplifying
y = -1.333333333
Solution
y = {-8, -1.333333333}

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