To solve this equation, we first need to expand the expression by multiplying each term in the first parentheses by each term in the second parentheses:

(3y - 7) (5y - 0.1)
= 3y 5y - 3y 0.1 - 7 5y - 7 * 0.1
= 15y^2 - 0.3y - 35y - 0.7
= 15y^2 - 35.3y - 0.7

Now, we have the expanded expression as 15y^2 - 35.3y - 0.7.

To find the values of y that satisfy the equation (15y^2 - 35.3y - 0.7 = 0), we can either try to factorize it or use the quadratic formula.

Using the quadratic formula:
y = (-(-35.3) ± √((-35.3)^2 - 415(-0.7))) / (2*15)
y = (35.3 ± √((1249.09 + 42))) / 30
y = (35.3 ± √(1291.09)) / 30
y = (35.3 ± 35.96) / 30

There are two possible solutions:
y = (35.3 + 35.96) / 30 = 71.26 / 30 ≈ 2.3767
y = (35.3 - 35.96) / 30 = -0.66 / 30 ≈ -0.022

Therefore, the solutions to the equation are y ≈ 2.3767 and y ≈ -0.022.