(4y+5)(y+7)=-2(4y+5)

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Solution for (4y+5)(y+7)=-2(4y+5) equation: 


Simplifying
(4y + 5)(y + 7) = -2(4y + 5)

Reorder the terms:
(5 + 4y)(y + 7) = -2(4y + 5)

Reorder the terms:
(5 + 4y)(7 + y) = -2(4y + 5)

Multiply (5 + 4y) * (7 + y)
(5(7 + y) + 4y * (7 + y)) = -2(4y + 5)
((7 * 5 + y * 5) + 4y * (7 + y)) = -2(4y + 5)
((35 + 5y) + 4y * (7 + y)) = -2(4y + 5)
(35 + 5y + (7 * 4y + y * 4y)) = -2(4y + 5)
(35 + 5y + (28y + 4y2)) = -2(4y + 5)

Combine like terms: 5y + 28y = 33y
(35 + 33y + 4y2) = -2(4y + 5)

Reorder the terms:
35 + 33y + 4y2 = -2(5 + 4y)
35 + 33y + 4y2 = (5 * -2 + 4y * -2)
35 + 33y + 4y2 = (-10 + -8y)

Solving
35 + 33y + 4y2 = -10 + -8y

Solving for variable 'y'.

Reorder the terms:
35 + 10 + 33y + 8y + 4y2 = -10 + -8y + 10 + 8y

Combine like terms: 35 + 10 = 45
45 + 33y + 8y + 4y2 = -10 + -8y + 10 + 8y

Combine like terms: 33y + 8y = 41y
45 + 41y + 4y2 = -10 + -8y + 10 + 8y

Reorder the terms:
45 + 41y + 4y2 = -10 + 10 + -8y + 8y

Combine like terms: -10 + 10 = 0
45 + 41y + 4y2 = 0 + -8y + 8y
45 + 41y + 4y2 = -8y + 8y

Combine like terms: -8y + 8y = 0
45 + 41y + 4y2 = 0

Factor a trinomial.
(9 + y)(5 + 4y) = 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 '(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 = {-9, -1.25}

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