To solve this equation, we need to simplify both sides and then solve for x.

First, let's simplify both sides:

4*0.5^(x(x+3)) = 0.25^(2x)

4 * 0.5^(x^2 + 3x) = (0.5^2)^(2x)

4 * 0.5^(x^2 + 3x) = 0.5^(4x)

Now, since the bases are the same, we can set the exponents equal to each other:

x^2 + 3x = 4x

x^2 + 3x - 4x = 0

x^2 - x = 0

x(x-1) = 0

So, x = 0 or x = 1.

Therefore, the solutions to the equation are x = 0 or x = 1.