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

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


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

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

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

Multiply (4 + 5y) * (5 + y)
(4(5 + y) + 5y * (5 + y)) = -4(5y + 4)
((5 * 4 + y * 4) + 5y * (5 + y)) = -4(5y + 4)
((20 + 4y) + 5y * (5 + y)) = -4(5y + 4)
(20 + 4y + (5 * 5y + y * 5y)) = -4(5y + 4)
(20 + 4y + (25y + 5y2)) = -4(5y + 4)

Combine like terms: 4y + 25y = 29y
(20 + 29y + 5y2) = -4(5y + 4)

Reorder the terms:
20 + 29y + 5y2 = -4(4 + 5y)
20 + 29y + 5y2 = (4 * -4 + 5y * -4)
20 + 29y + 5y2 = (-16 + -20y)

Solving
20 + 29y + 5y2 = -16 + -20y

Solving for variable 'y'.

Reorder the terms:
20 + 16 + 29y + 20y + 5y2 = -16 + -20y + 16 + 20y

Combine like terms: 20 + 16 = 36
36 + 29y + 20y + 5y2 = -16 + -20y + 16 + 20y

Combine like terms: 29y + 20y = 49y
36 + 49y + 5y2 = -16 + -20y + 16 + 20y

Reorder the terms:
36 + 49y + 5y2 = -16 + 16 + -20y + 20y

Combine like terms: -16 + 16 = 0
36 + 49y + 5y2 = 0 + -20y + 20y
36 + 49y + 5y2 = -20y + 20y

Combine like terms: -20y + 20y = 0
36 + 49y + 5y2 = 0

Factor a trinomial.
(9 + y)(4 + 5y) = 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 '(4 + 5y)' equal to zero and attempt to solve:

Simplifying
4 + 5y = 0

Solving
4 + 5y = 0

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

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

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

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

Divide each side by '5'.
y = -0.8

Simplifying
y = -0.8
Solution
y = {-9, -0.8}

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