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

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


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

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

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

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

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

Reorder the terms:
35 + 33y + 4y2 = -4(5 + 4y)
35 + 33y + 4y2 = (5 * -4 + 4y * -4)
35 + 33y + 4y2 = (-20 + -16y)

Solving
35 + 33y + 4y2 = -20 + -16y

Solving for variable 'y'.

Reorder the terms:
35 + 20 + 33y + 16y + 4y2 = -20 + -16y + 20 + 16y

Combine like terms: 35 + 20 = 55
55 + 33y + 16y + 4y2 = -20 + -16y + 20 + 16y

Combine like terms: 33y + 16y = 49y
55 + 49y + 4y2 = -20 + -16y + 20 + 16y

Reorder the terms:
55 + 49y + 4y2 = -20 + 20 + -16y + 16y

Combine like terms: -20 + 20 = 0
55 + 49y + 4y2 = 0 + -16y + 16y
55 + 49y + 4y2 = -16y + 16y

Combine like terms: -16y + 16y = 0
55 + 49y + 4y2 = 0

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


Subproblem 1
Set the factor '(11 + y)' equal to zero and attempt to solve:

Simplifying
11 + y = 0

Solving
11 + y = 0

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

Add '-11' to each side of the equation.
11 + -11 + y = 0 + -11

Combine like terms: 11 + -11 = 0
0 + y = 0 + -11
y = 0 + -11

Combine like terms: 0 + -11 = -11
y = -11

Simplifying
y = -11

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 = {-11, -1.25}

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