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

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


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

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

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

Multiply (5 + 4y) * (4 + y)
(5(4 + y) + 4y * (4 + y)) = -5(4y + 5)
((4 * 5 + y * 5) + 4y * (4 + y)) = -5(4y + 5)
((20 + 5y) + 4y * (4 + y)) = -5(4y + 5)
(20 + 5y + (4 * 4y + y * 4y)) = -5(4y + 5)
(20 + 5y + (16y + 4y2)) = -5(4y + 5)

Combine like terms: 5y + 16y = 21y
(20 + 21y + 4y2) = -5(4y + 5)

Reorder the terms:
20 + 21y + 4y2 = -5(5 + 4y)
20 + 21y + 4y2 = (5 * -5 + 4y * -5)
20 + 21y + 4y2 = (-25 + -20y)

Solving
20 + 21y + 4y2 = -25 + -20y

Solving for variable 'y'.

Reorder the terms:
20 + 25 + 21y + 20y + 4y2 = -25 + -20y + 25 + 20y

Combine like terms: 20 + 25 = 45
45 + 21y + 20y + 4y2 = -25 + -20y + 25 + 20y

Combine like terms: 21y + 20y = 41y
45 + 41y + 4y2 = -25 + -20y + 25 + 20y

Reorder the terms:
45 + 41y + 4y2 = -25 + 25 + -20y + 20y

Combine like terms: -25 + 25 = 0
45 + 41y + 4y2 = 0 + -20y + 20y
45 + 41y + 4y2 = -20y + 20y

Combine like terms: -20y + 20y = 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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