$$\frac{2+3x}{5}=\frac{15-2x}{6}$$
$x = \frac{9}{4} = 2\frac{1}{4} = 2.25$
$$6\left(2+3x\right)=5\left(15-2x\right)$$
$$12+18x=5\left(15-2x\right)$$
$$12+18x=75-10x$$
$$12+18x+10x=75$$
$$12+28x=75$$
$$28x=75-12$$
$$28x=63$$
$$x=\frac{63}{28}$$
$$x=\frac{9}{4}$$
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