To solve this equation, we will first distribute the coefficients:

4/7 0.56 - 4.2(4/7)y + 0.4 = 5/13 0.52 - 6.5(5/13)y

Next, we will simplify the equation by multiplying the fractions:

0.32 - 2.4y + 0.4 = 0.2 - 2.5y

Now, we will combine like terms to simplify the equation further:

0.72 - 2.4y = 0.2 - 2.5y

Next, we will move all terms involving y to one side of the equation:

2.3y = 0.2 - 0.72

2.3y = -0.52

Now we can solve for y by dividing by 2.3 on both sides:

y = -0.52 / 2.3

y = -0.226

Therefore, the solution to the equation is y = -0.226.