Let's simplify the left side of the equation first using the distributive property:

(3y - 1) × (y + 3)
= 3y(y) + 3y(3) - 1(y) - 1(3)
= 3y^2 + 9y - y - 3
= 3y^2 + 8y - 3

Now let's simplify the right side of the equation:

y(6y + 1)
= 6y^2 + y

Now we can set the two sides of the equation equal to each other and solve for y:

3y^2 + 8y - 3 = 6y^2 + y

Rearranging terms:

3y^2 - 6y^2 + 8y - y - 3 = 0
-3y^2 + 7y - 3 = 0

This quadratic equation doesn't simplify easily, so we could solve it by using the quadratic formula:

y = [-b ± sqrt(b^2 - 4ac)] / 2a

In this case, a = -3, b = 7, and c = -3. Plugging in the values:

y = [-7 ± sqrt(7^2 - 4(-3)(-3))] / 2(-3)
y = [-7 ± sqrt(49 - 36)] / -6
y = [-7 ± sqrt(13)] / -6

So the solutions for y are:

y = (-7 + sqrt(13)) / -6 and y = (-7 - sqrt(13)) / -6