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

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


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

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

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

Multiply (4 + 3y) * (4 + y)
(4(4 + y) + 3y * (4 + y)) = -5(3y + 4)
((4 * 4 + y * 4) + 3y * (4 + y)) = -5(3y + 4)
((16 + 4y) + 3y * (4 + y)) = -5(3y + 4)
(16 + 4y + (4 * 3y + y * 3y)) = -5(3y + 4)
(16 + 4y + (12y + 3y2)) = -5(3y + 4)

Combine like terms: 4y + 12y = 16y
(16 + 16y + 3y2) = -5(3y + 4)

Reorder the terms:
16 + 16y + 3y2 = -5(4 + 3y)
16 + 16y + 3y2 = (4 * -5 + 3y * -5)
16 + 16y + 3y2 = (-20 + -15y)

Solving
16 + 16y + 3y2 = -20 + -15y

Solving for variable 'y'.

Reorder the terms:
16 + 20 + 16y + 15y + 3y2 = -20 + -15y + 20 + 15y

Combine like terms: 16 + 20 = 36
36 + 16y + 15y + 3y2 = -20 + -15y + 20 + 15y

Combine like terms: 16y + 15y = 31y
36 + 31y + 3y2 = -20 + -15y + 20 + 15y

Reorder the terms:
36 + 31y + 3y2 = -20 + 20 + -15y + 15y

Combine like terms: -20 + 20 = 0
36 + 31y + 3y2 = 0 + -15y + 15y
36 + 31y + 3y2 = -15y + 15y

Combine like terms: -15y + 15y = 0
36 + 31y + 3y2 = 0

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


Subproblem 1
Set the factor '(9 + y)' equal to zero and attempt to solve:

Simplifying
9 + y = 0

Solving
9 + y = 0

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

Add '-9' to each side of the equation.
9 + -9 + y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + y = 0 + -9
y = 0 + -9

Combine like terms: 0 + -9 = -9
y = -9

Simplifying
y = -9

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 = {-9, -1.333333333}

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