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

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


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

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

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

Multiply (3 + 2y) * (4 + y)
(3(4 + y) + 2y * (4 + y)) = -3(2y + 3)
((4 * 3 + y * 3) + 2y * (4 + y)) = -3(2y + 3)
((12 + 3y) + 2y * (4 + y)) = -3(2y + 3)
(12 + 3y + (4 * 2y + y * 2y)) = -3(2y + 3)
(12 + 3y + (8y + 2y2)) = -3(2y + 3)

Combine like terms: 3y + 8y = 11y
(12 + 11y + 2y2) = -3(2y + 3)

Reorder the terms:
12 + 11y + 2y2 = -3(3 + 2y)
12 + 11y + 2y2 = (3 * -3 + 2y * -3)
12 + 11y + 2y2 = (-9 + -6y)

Solving
12 + 11y + 2y2 = -9 + -6y

Solving for variable 'y'.

Reorder the terms:
12 + 9 + 11y + 6y + 2y2 = -9 + -6y + 9 + 6y

Combine like terms: 12 + 9 = 21
21 + 11y + 6y + 2y2 = -9 + -6y + 9 + 6y

Combine like terms: 11y + 6y = 17y
21 + 17y + 2y2 = -9 + -6y + 9 + 6y

Reorder the terms:
21 + 17y + 2y2 = -9 + 9 + -6y + 6y

Combine like terms: -9 + 9 = 0
21 + 17y + 2y2 = 0 + -6y + 6y
21 + 17y + 2y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
21 + 17y + 2y2 = 0

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

Simplifying
3 + 2y = 0

Solving
3 + 2y = 0

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

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

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

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

Divide each side by '2'.
y = -1.5

Simplifying
y = -1.5
Solution
y = {-7, -1.5}

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