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

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


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

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

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

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

Combine like terms: 2y + 6y = 8y
(4 + 8y + 3y2) = -4(3y + 2)

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

Solving
4 + 8y + 3y2 = -8 + -12y

Solving for variable 'y'.

Reorder the terms:
4 + 8 + 8y + 12y + 3y2 = -8 + -12y + 8 + 12y

Combine like terms: 4 + 8 = 12
12 + 8y + 12y + 3y2 = -8 + -12y + 8 + 12y

Combine like terms: 8y + 12y = 20y
12 + 20y + 3y2 = -8 + -12y + 8 + 12y

Reorder the terms:
12 + 20y + 3y2 = -8 + 8 + -12y + 12y

Combine like terms: -8 + 8 = 0
12 + 20y + 3y2 = 0 + -12y + 12y
12 + 20y + 3y2 = -12y + 12y

Combine like terms: -12y + 12y = 0
12 + 20y + 3y2 = 0

Factor a trinomial.
(6 + y)(2 + 3y) = 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 '(2 + 3y)' equal to zero and attempt to solve:

Simplifying
2 + 3y = 0

Solving
2 + 3y = 0

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

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

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

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

Divide each side by '3'.
y = -0.6666666667

Simplifying
y = -0.6666666667
Solution
y = {-6, -0.6666666667}

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