Answer
$-\frac{3}{4}$
Work Step by Step
Step 1. Provided $x\ne0,2$, multiply $x^2-2x=x(x-2)$ on both sides, we have $4x^2+3(x-2)=-6$
Step 2. Expand the equation to get $4x^2+3x-6=-6\longrightarrow x(4x+3)=0$
Step 3. The above gives $x=0$ and $x=-\frac{3}{4}$, however, $x\ne 0$ is the starting condition, thus, the only solution is $x=-\frac{3}{4}$
