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

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


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

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

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

Multiply (4 + 3y) * (3 + y)
(4(3 + y) + 3y * (3 + y)) = -4(3y + 4)
((3 * 4 + y * 4) + 3y * (3 + y)) = -4(3y + 4)
((12 + 4y) + 3y * (3 + y)) = -4(3y + 4)
(12 + 4y + (3 * 3y + y * 3y)) = -4(3y + 4)
(12 + 4y + (9y + 3y2)) = -4(3y + 4)

Combine like terms: 4y + 9y = 13y
(12 + 13y + 3y2) = -4(3y + 4)

Reorder the terms:
12 + 13y + 3y2 = -4(4 + 3y)
12 + 13y + 3y2 = (4 * -4 + 3y * -4)
12 + 13y + 3y2 = (-16 + -12y)

Solving
12 + 13y + 3y2 = -16 + -12y

Solving for variable 'y'.

Reorder the terms:
12 + 16 + 13y + 12y + 3y2 = -16 + -12y + 16 + 12y

Combine like terms: 12 + 16 = 28
28 + 13y + 12y + 3y2 = -16 + -12y + 16 + 12y

Combine like terms: 13y + 12y = 25y
28 + 25y + 3y2 = -16 + -12y + 16 + 12y

Reorder the terms:
28 + 25y + 3y2 = -16 + 16 + -12y + 12y

Combine like terms: -16 + 16 = 0
28 + 25y + 3y2 = 0 + -12y + 12y
28 + 25y + 3y2 = -12y + 12y

Combine like terms: -12y + 12y = 0
28 + 25y + 3y2 = 0

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


Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

Solving
7 + y = 0

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

Add '-7' to each side of the equation.
7 + -7 + y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + y = 0 + -7
y = 0 + -7

Combine like terms: 0 + -7 = -7
y = -7

Simplifying
y = -7

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 = {-7, -1.333333333}

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