Answer
$\color{blue}{\left\{0, \frac{3}{4}\right\}}$
Work Step by Step
Subtract $6x$ to both sides of the equation to obtain:
$8x^2-6x=6x-6x
\\8x^2-6x=0$
Factor out $x$ to obtain:
$x(8x-6)=0$
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 $8x-6=0$
Solve each equation to obtain:
$x=0$
or
$8x-6=0
\\8x=0+6
\\8x=6
\\\frac{8x}{8}=\frac{6}{8}
\\x=\frac{3}{4}$
Therefore, the solution set is $\color{blue}{\left\{0, \frac{3}{4}\right\}}$.
