(3y+2)(y+7)=-4(3y+2)

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Solution for (3y+2)(y+7)=-4(3y+2) equation: 


Simplifying
(3y + 2)(y + 7) = -4(3y + 2)

Reorder the terms:
(2 + 3y)(y + 7) = -4(3y + 2)

Reorder the terms:
(2 + 3y)(7 + y) = -4(3y + 2)

Multiply (2 + 3y) * (7 + y)
(2(7 + y) + 3y * (7 + y)) = -4(3y + 2)
((7 * 2 + y * 2) + 3y * (7 + y)) = -4(3y + 2)
((14 + 2y) + 3y * (7 + y)) = -4(3y + 2)
(14 + 2y + (7 * 3y + y * 3y)) = -4(3y + 2)
(14 + 2y + (21y + 3y2)) = -4(3y + 2)

Combine like terms: 2y + 21y = 23y
(14 + 23y + 3y2) = -4(3y + 2)

Reorder the terms:
14 + 23y + 3y2 = -4(2 + 3y)
14 + 23y + 3y2 = (2 * -4 + 3y * -4)
14 + 23y + 3y2 = (-8 + -12y)

Solving
14 + 23y + 3y2 = -8 + -12y

Solving for variable 'y'.

Reorder the terms:
14 + 8 + 23y + 12y + 3y2 = -8 + -12y + 8 + 12y

Combine like terms: 14 + 8 = 22
22 + 23y + 12y + 3y2 = -8 + -12y + 8 + 12y

Combine like terms: 23y + 12y = 35y
22 + 35y + 3y2 = -8 + -12y + 8 + 12y

Reorder the terms:
22 + 35y + 3y2 = -8 + 8 + -12y + 12y

Combine like terms: -8 + 8 = 0
22 + 35y + 3y2 = 0 + -12y + 12y
22 + 35y + 3y2 = -12y + 12y

Combine like terms: -12y + 12y = 0
22 + 35y + 3y2 = 0

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


Subproblem 1
Set the factor '(11 + y)' equal to zero and attempt to solve:

Simplifying
11 + y = 0

Solving
11 + y = 0

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

Add '-11' to each side of the equation.
11 + -11 + y = 0 + -11

Combine like terms: 11 + -11 = 0
0 + y = 0 + -11
y = 0 + -11

Combine like terms: 0 + -11 = -11
y = -11

Simplifying
y = -11

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 = {-11, -0.6666666667}

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