(5y+3)(y+7)=-5(5y+3)

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Solution for (5y+3)(y+7)=-5(5y+3) equation: 


Simplifying
(5y + 3)(y + 7) = -5(5y + 3)

Reorder the terms:
(3 + 5y)(y + 7) = -5(5y + 3)

Reorder the terms:
(3 + 5y)(7 + y) = -5(5y + 3)

Multiply (3 + 5y) * (7 + y)
(3(7 + y) + 5y * (7 + y)) = -5(5y + 3)
((7 * 3 + y * 3) + 5y * (7 + y)) = -5(5y + 3)
((21 + 3y) + 5y * (7 + y)) = -5(5y + 3)
(21 + 3y + (7 * 5y + y * 5y)) = -5(5y + 3)
(21 + 3y + (35y + 5y2)) = -5(5y + 3)

Combine like terms: 3y + 35y = 38y
(21 + 38y + 5y2) = -5(5y + 3)

Reorder the terms:
21 + 38y + 5y2 = -5(3 + 5y)
21 + 38y + 5y2 = (3 * -5 + 5y * -5)
21 + 38y + 5y2 = (-15 + -25y)

Solving
21 + 38y + 5y2 = -15 + -25y

Solving for variable 'y'.

Reorder the terms:
21 + 15 + 38y + 25y + 5y2 = -15 + -25y + 15 + 25y

Combine like terms: 21 + 15 = 36
36 + 38y + 25y + 5y2 = -15 + -25y + 15 + 25y

Combine like terms: 38y + 25y = 63y
36 + 63y + 5y2 = -15 + -25y + 15 + 25y

Reorder the terms:
36 + 63y + 5y2 = -15 + 15 + -25y + 25y

Combine like terms: -15 + 15 = 0
36 + 63y + 5y2 = 0 + -25y + 25y
36 + 63y + 5y2 = -25y + 25y

Combine like terms: -25y + 25y = 0
36 + 63y + 5y2 = 0

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


Subproblem 1
Set the factor '(12 + y)' equal to zero and attempt to solve:

Simplifying
12 + y = 0

Solving
12 + y = 0

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

Add '-12' to each side of the equation.
12 + -12 + y = 0 + -12

Combine like terms: 12 + -12 = 0
0 + y = 0 + -12
y = 0 + -12

Combine like terms: 0 + -12 = -12
y = -12

Simplifying
y = -12

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 = {-12, -0.6}

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