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

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


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

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

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

Multiply (5 + 3y) * (3 + y)
(5(3 + y) + 3y * (3 + y)) = 7
((3 * 5 + y * 5) + 3y * (3 + y)) = 7
((15 + 5y) + 3y * (3 + y)) = 7
(15 + 5y + (3 * 3y + y * 3y)) = 7
(15 + 5y + (9y + 3y2)) = 7

Combine like terms: 5y + 9y = 14y
(15 + 14y + 3y2) = 7

Solving
15 + 14y + 3y2 = 7

Solving for variable 'y'.

Reorder the terms:
15 + -7 + 14y + 3y2 = 7 + -7

Combine like terms: 15 + -7 = 8
8 + 14y + 3y2 = 7 + -7

Combine like terms: 7 + -7 = 0
8 + 14y + 3y2 = 0

Factor a trinomial.
(4 + y)(2 + 3y) = 0


Subproblem 1
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 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 + y = 0 + -4

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

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

Simplifying
y = -4

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

Simplifying
2 + 3y = 0

Solving
2 + 3y = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3y = 0 + -2
3y = 0 + -2

Combine like terms: 0 + -2 = -2
3y = -2

Divide each side by '3'.
y = -0.6666666667

Simplifying
y = -0.6666666667
Solution
y = {-4, -0.6666666667}

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