Let's first simplify the left side of the equation:

X(x-5)+3x(x-3)
= x^2 - 5x + 3x^2 - 9x
= x^2 + 3x^2 - 5x - 9x
= 4x^2 - 14x

So, the left side of the equation simplifies to 4x^2 - 14x. Now, let's simplify the right side of the equation:

2x^2 + 4x

The right side of the equation is already simplified as 2x^2 + 4x.

Now, we need to set the simplified left side of the equation equal to the simplified right side of the equation:

4x^2 - 14x = 2x^2 + 4x

Now, we can solve for x:

4x^2 - 14x = 2x^2 + 4x
2x^2 - 14x - 4x^2 + 4x = 0
-2x^2 - 10x = 0
-2x(x + 5) = 0

Setting each factor to zero:

-2x = 0
x = 0

x + 5 = 0
x = -5

Therefore, the solutions to the equation are x = 0 and x = -5.