Answer
$\color{blue}{\left\{0, \frac{5}{3}\right\}}$
Work Step by Step
Subtract $10x$ to both sides of the equation to obtain:
$6x^2-10x=10x-10x
\\6x^2-10x=0$
Factor out $x$ to obtain:
$x(6x-10)=0$
RECALL:
The Zero-Factor Property states that if $ab=0$, then $a=0$ or $b=0$, or both are zero.
Use the Zero-Factor Property by equating each factor to zero to obtain:
$x=0$ or $6x-10=0$
Solve each equation to obtain:
$x=0$
or
$6x-10=0
\\6x=0+10
\\6x=10
\\\frac{6x}{6}=\frac{10}{6}
\\x=\frac{5}{3}$
Therefore, the solution set is $\color{blue}{\left\{0, \frac{5}{3}\right\}}$.
