(5y+3)(y+3)=-4(5y+3)

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Solution for (5y+3)(y+3)=-4(5y+3) equation: 


Simplifying
(5y + 3)(y + 3) = -4(5y + 3)

Reorder the terms:
(3 + 5y)(y + 3) = -4(5y + 3)

Reorder the terms:
(3 + 5y)(3 + y) = -4(5y + 3)

Multiply (3 + 5y) * (3 + y)
(3(3 + y) + 5y * (3 + y)) = -4(5y + 3)
((3 * 3 + y * 3) + 5y * (3 + y)) = -4(5y + 3)
((9 + 3y) + 5y * (3 + y)) = -4(5y + 3)
(9 + 3y + (3 * 5y + y * 5y)) = -4(5y + 3)
(9 + 3y + (15y + 5y2)) = -4(5y + 3)

Combine like terms: 3y + 15y = 18y
(9 + 18y + 5y2) = -4(5y + 3)

Reorder the terms:
9 + 18y + 5y2 = -4(3 + 5y)
9 + 18y + 5y2 = (3 * -4 + 5y * -4)
9 + 18y + 5y2 = (-12 + -20y)

Solving
9 + 18y + 5y2 = -12 + -20y

Solving for variable 'y'.

Reorder the terms:
9 + 12 + 18y + 20y + 5y2 = -12 + -20y + 12 + 20y

Combine like terms: 9 + 12 = 21
21 + 18y + 20y + 5y2 = -12 + -20y + 12 + 20y

Combine like terms: 18y + 20y = 38y
21 + 38y + 5y2 = -12 + -20y + 12 + 20y

Reorder the terms:
21 + 38y + 5y2 = -12 + 12 + -20y + 20y

Combine like terms: -12 + 12 = 0
21 + 38y + 5y2 = 0 + -20y + 20y
21 + 38y + 5y2 = -20y + 20y

Combine like terms: -20y + 20y = 0
21 + 38y + 5y2 = 0

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


Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

Solving
7 + y = 0

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

Add '-7' to each side of the equation.
7 + -7 + y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + y = 0 + -7
y = 0 + -7

Combine like terms: 0 + -7 = -7
y = -7

Simplifying
y = -7

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 = {-7, -0.6}

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