## Intermediate Algebra: Connecting Concepts through Application

$\color{blue}{\left\{0, \frac{3}{4}\right\}}$
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 $\color{blue}{\left\{0, \frac{3}{4}\right\}}$.