$$\frac{5(3-2x)}{4}+\frac{3x+8}{6}=3(x+1)$$
$x=\frac{5}{12}\approx 0.416666667$
$$3\times 5\left(3-2x\right)+2\left(3x+8\right)=36\left(x+1\right)$$
$$15\left(3-2x\right)+2\left(3x+8\right)=36\left(x+1\right)$$
$$45-30x+2\left(3x+8\right)=36\left(x+1\right)$$
$$45-30x+6x+16=36\left(x+1\right)$$
$$45-24x+16=36\left(x+1\right)$$
$$61-24x=36\left(x+1\right)$$
$$61-24x=36x+36$$
$$61-24x-36x=36$$
$$61-60x=36$$
$$-60x=36-61$$
$$-60x=-25$$
$$x=\frac{-25}{-60}$$
$$x=\frac{5}{12}$$
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