$$2(x+3)(x-2)-7=(2x+1)(x-3)$$
$x = \frac{16}{7} = 2\frac{2}{7} \approx 2.285714286$
$$\left(2x+6\right)\left(x-2\right)-7=\left(2x+1\right)\left(x-3\right)$$
$$2x^{2}+2x-12-7=\left(2x+1\right)\left(x-3\right)$$
$$2x^{2}+2x-19=\left(2x+1\right)\left(x-3\right)$$
$$2x^{2}+2x-19=2x^{2}-5x-3$$
$$2x^{2}+2x-19-2x^{2}=-5x-3$$
$$2x-19=-5x-3$$
$$2x-19+5x=-3$$
$$7x-19=-3$$
$$7x=-3+19$$
$$7x=16$$
$$x=\frac{16}{7}$$
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