Let's first distribute the terms on both sides of the equation:

0.4x(5) + 0.4x(3x) + 0.6 = 0.2x(6x) - 0.2x(3)

0.4x(5) = 2x
0.4x(3x) = 1.2x^2
0.2x(6x) = 1.2x^2
0.2x(3) = 0.6x

Substitute these back into the original equation:

2x + 1.2x^2 + 0.6 = 1.2x^2 - 0.6x

Rearrange the terms to simplify the equation:

2x + 1.2x^2 + 0.6 = 1.2x^2 - 0.6x

2x + 0.6 = -0.6x

Now, solve for x:

2x + 0.6 = -0.6x
2x + 0.6x = -0.6
2.6x = -0.6
x = -0.6 / 2.6
x = -0.23

Therefore, the solution to the equation is x = -0.23.