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

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

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

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

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

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

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

Reorder the terms:
21 + 17y + 2y2 = 2(3 + 2y)
21 + 17y + 2y2 = (3 * 2 + 2y * 2)
21 + 17y + 2y2 = (6 + 4y)

Solving
21 + 17y + 2y2 = 6 + 4y

Solving for variable 'y'.

Reorder the terms:
21 + -6 + 17y + -4y + 2y2 = 6 + 4y + -6 + -4y

Combine like terms: 21 + -6 = 15
15 + 17y + -4y + 2y2 = 6 + 4y + -6 + -4y

Combine like terms: 17y + -4y = 13y
15 + 13y + 2y2 = 6 + 4y + -6 + -4y

Reorder the terms:
15 + 13y + 2y2 = 6 + -6 + 4y + -4y

Combine like terms: 6 + -6 = 0
15 + 13y + 2y2 = 0 + 4y + -4y
15 + 13y + 2y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
15 + 13y + 2y2 = 0

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

Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

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

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

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

Simplifying
y = -5
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 = {-5, -1.5}