To solve this equation, we will first expand the left side of the equation:

(5y - 7) (2y - 0.4)
= 5y 2y + 5y (-0.4) - 7 2y - 7 * (-0.4)
= 10y^2 - 2y - 14y + 2.8
= 10y^2 - 16y + 2.8

Now we set this expression equal to 0 and solve for y:

10y^2 - 16y + 2.8 = 0

We can simplify this quadratic equation by dividing all terms by 2.8 to make it easier to solve:

10y^2/2.8 - 16y/2.8 + 2.8/2.8 = 0/2.8
3.5714y^2 - 5.7143y + 1 = 0

This quadratic equation does not have simple integer solutions, so we can use the quadratic formula to find the roots:

y = (-(-5.7143) ± √((-5.7143)^2 - 43.57141)) / 2*3.5714
y = (5.7143 ± √(32.6531 - 14.2856)) / 7.1428
y = (5.7143 ± √18.3675) / 7.1428
y = (5.7143 ± 4.2872) / 7.1428

This gives us two possible values for y:

y = (5.7143 + 4.2872) / 7.1428 ≈ 1.2511
y = (5.7143 - 4.2872) / 7.1428 ≈ 0.2827

Therefore, the solutions to the equation are approximately y ≈ 1.2511 and y ≈ 0.2827.