(2y+3)(y+7)=-3(2y+3)

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Solution for (2y+3)(y+7)=-3(2y+3) equation: 


Simplifying
(2y + 3)(y + 7) = -3(2y + 3)

Reorder the terms:
(3 + 2y)(y + 7) = -3(2y + 3)

Reorder the terms:
(3 + 2y)(7 + y) = -3(2y + 3)

Multiply (3 + 2y) * (7 + y)
(3(7 + y) + 2y * (7 + y)) = -3(2y + 3)
((7 * 3 + y * 3) + 2y * (7 + y)) = -3(2y + 3)
((21 + 3y) + 2y * (7 + y)) = -3(2y + 3)
(21 + 3y + (7 * 2y + y * 2y)) = -3(2y + 3)
(21 + 3y + (14y + 2y2)) = -3(2y + 3)

Combine like terms: 3y + 14y = 17y
(21 + 17y + 2y2) = -3(2y + 3)

Reorder the terms:
21 + 17y + 2y2 = -3(3 + 2y)
21 + 17y + 2y2 = (3 * -3 + 2y * -3)
21 + 17y + 2y2 = (-9 + -6y)

Solving
21 + 17y + 2y2 = -9 + -6y

Solving for variable 'y'.

Reorder the terms:
21 + 9 + 17y + 6y + 2y2 = -9 + -6y + 9 + 6y

Combine like terms: 21 + 9 = 30
30 + 17y + 6y + 2y2 = -9 + -6y + 9 + 6y

Combine like terms: 17y + 6y = 23y
30 + 23y + 2y2 = -9 + -6y + 9 + 6y

Reorder the terms:
30 + 23y + 2y2 = -9 + 9 + -6y + 6y

Combine like terms: -9 + 9 = 0
30 + 23y + 2y2 = 0 + -6y + 6y
30 + 23y + 2y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
30 + 23y + 2y2 = 0

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


Subproblem 1
Set the factor '(10 + y)' equal to zero and attempt to solve:

Simplifying
10 + y = 0

Solving
10 + y = 0

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

Add '-10' to each side of the equation.
10 + -10 + y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + y = 0 + -10
y = 0 + -10

Combine like terms: 0 + -10 = -10
y = -10

Simplifying
y = -10

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

Simplifying
3 + 2y = 0

Solving
3 + 2y = 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 + 2y = 0 + -3

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

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

Divide each side by '2'.
y = -1.5

Simplifying
y = -1.5
Solution
y = {-10, -1.5}

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