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

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


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

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

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

Multiply (3 + 5y) * (5 + y)
(3(5 + y) + 5y * (5 + y)) = -3(5y + 3)
((5 * 3 + y * 3) + 5y * (5 + y)) = -3(5y + 3)
((15 + 3y) + 5y * (5 + y)) = -3(5y + 3)
(15 + 3y + (5 * 5y + y * 5y)) = -3(5y + 3)
(15 + 3y + (25y + 5y2)) = -3(5y + 3)

Combine like terms: 3y + 25y = 28y
(15 + 28y + 5y2) = -3(5y + 3)

Reorder the terms:
15 + 28y + 5y2 = -3(3 + 5y)
15 + 28y + 5y2 = (3 * -3 + 5y * -3)
15 + 28y + 5y2 = (-9 + -15y)

Solving
15 + 28y + 5y2 = -9 + -15y

Solving for variable 'y'.

Reorder the terms:
15 + 9 + 28y + 15y + 5y2 = -9 + -15y + 9 + 15y

Combine like terms: 15 + 9 = 24
24 + 28y + 15y + 5y2 = -9 + -15y + 9 + 15y

Combine like terms: 28y + 15y = 43y
24 + 43y + 5y2 = -9 + -15y + 9 + 15y

Reorder the terms:
24 + 43y + 5y2 = -9 + 9 + -15y + 15y

Combine like terms: -9 + 9 = 0
24 + 43y + 5y2 = 0 + -15y + 15y
24 + 43y + 5y2 = -15y + 15y

Combine like terms: -15y + 15y = 0
24 + 43y + 5y2 = 0

Factor a trinomial.
(8 + y)(3 + 5y) = 0


Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve:

Simplifying
8 + y = 0

Solving
8 + y = 0

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

Add '-8' to each side of the equation.
8 + -8 + y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + y = 0 + -8
y = 0 + -8

Combine like terms: 0 + -8 = -8
y = -8

Simplifying
y = -8

Subproblem 2
Set the factor '(3 + 5y)' equal to zero and attempt to solve:

Simplifying
3 + 5y = 0

Solving
3 + 5y = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5y = 0 + -3
5y = 0 + -3

Combine like terms: 0 + -3 = -3
5y = -3

Divide each side by '5'.
y = -0.6

Simplifying
y = -0.6
Solution
y = {-8, -0.6}

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