(4y+5)(y+3)=-2(4y+5)

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Solution for (4y+5)(y+3)=-2(4y+5) equation: 


Simplifying
(4y + 5)(y + 3) = -2(4y + 5)

Reorder the terms:
(5 + 4y)(y + 3) = -2(4y + 5)

Reorder the terms:
(5 + 4y)(3 + y) = -2(4y + 5)

Multiply (5 + 4y) * (3 + y)
(5(3 + y) + 4y * (3 + y)) = -2(4y + 5)
((3 * 5 + y * 5) + 4y * (3 + y)) = -2(4y + 5)
((15 + 5y) + 4y * (3 + y)) = -2(4y + 5)
(15 + 5y + (3 * 4y + y * 4y)) = -2(4y + 5)
(15 + 5y + (12y + 4y2)) = -2(4y + 5)

Combine like terms: 5y + 12y = 17y
(15 + 17y + 4y2) = -2(4y + 5)

Reorder the terms:
15 + 17y + 4y2 = -2(5 + 4y)
15 + 17y + 4y2 = (5 * -2 + 4y * -2)
15 + 17y + 4y2 = (-10 + -8y)

Solving
15 + 17y + 4y2 = -10 + -8y

Solving for variable 'y'.

Reorder the terms:
15 + 10 + 17y + 8y + 4y2 = -10 + -8y + 10 + 8y

Combine like terms: 15 + 10 = 25
25 + 17y + 8y + 4y2 = -10 + -8y + 10 + 8y

Combine like terms: 17y + 8y = 25y
25 + 25y + 4y2 = -10 + -8y + 10 + 8y

Reorder the terms:
25 + 25y + 4y2 = -10 + 10 + -8y + 8y

Combine like terms: -10 + 10 = 0
25 + 25y + 4y2 = 0 + -8y + 8y
25 + 25y + 4y2 = -8y + 8y

Combine like terms: -8y + 8y = 0
25 + 25y + 4y2 = 0

Factor a trinomial.
(5 + y)(5 + 4y) = 0


Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + y = 0 + -5
y = 0 + -5

Combine like terms: 0 + -5 = -5
y = -5

Simplifying
y = -5

Subproblem 2
Set the factor '(5 + 4y)' equal to zero and attempt to solve:

Simplifying
5 + 4y = 0

Solving
5 + 4y = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4y = 0 + -5
4y = 0 + -5

Combine like terms: 0 + -5 = -5
4y = -5

Divide each side by '4'.
y = -1.25

Simplifying
y = -1.25
Solution
y = {-5, -1.25}

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