To solve this equation, we will first manipulate the bases to make them the same.

Using the property of exponents that states x^(a*b) = (x^a)^b, we can rewrite the equation as:

(7^2)^(4x+2) = 5^(3x+4) * 7^5x

Now we can simplify the left side of the equation:

7^4(4x+2) = 5^(3x+4) * 7^5x

28x + 8 = 5^(3x+4) * 7^5x

Next, we will rewrite 7^5x as (7^4)^x and apply the power rule of exponents:

28x + 8 = 5^(3x+4) * (7^4)^x

28x + 8 = 5^(3x+4) * 7^(4x)

Now we have the bases 5 and 7 the same, so we can write the equation as:

28x + 8 = 5^(3x+4) * 7^4x

Now we have the bases the same, so we can set the exponents equal to each other:

28x + 8 = 3x + 4 + 4x

28x + 8 = 7x + 4

21x = -4

x = -4/21

Therefore, the solution to the equation is x = -4/21.