Answer
$w=\frac{2}{3},w=\frac{5}{2}$
Work Step by Step
There is much work to be done here until the equation is simplified. The work speaks for itself! $$
\begin{aligned}
6 w^2-15 w&=4 w-10\\
6 w^2-15 w-4 w&+10=0\\
(6 w^2-15 w)-(4 w&-10)=0\\
3w(2 w-5)-2(2 w&-5)=0\\
(2 w-5)(3w-2)&= 0.
\end{aligned}
$$ Hence $$
\begin{aligned}
2 w-5& =0 \\
2w & =5 \\
w & =\frac{5}{2} \\
& =2.5 \\
3 w-2& =0 \\
3w & =2 \\
w & =\frac{2}{3}.
\end{aligned}
$$ Check
$$
\begin{aligned}
6 \cdot 2.5^2-15\cdot 2.5&\stackrel{?}{=}4\cdot 2.5-10 \\
0& =0\checkmark\\
6 \cdot \left(\frac{2}{3}\right)^2-15\cdot \frac{2}{3}&=4\cdot \frac{2}{3}-10 \\
-\frac{22}{3}& =-\frac{22}{3}\checkmark.
\end{aligned}
$$
