Appendix A - Equations and Inequalities - Page 417: 42

{$\frac{2}{3}$}

$9x^{2}-12x+4=0$ $9x^{2}-6x-6x+4=0$ $3x(3x-2)-2(3x-2)=0$ $(3x-2)(3x-2)=0$ $(3x-2)=0$ or $(3x-2)=0$ $x=\frac{2}{3}$ or $x=\frac{2}{3}$ Check: Substituting $x=\frac{2}{3}$ in the equation, $9(\frac{2}{3})^{2}-12(\frac{2}{3})+4=0$ $\frac{36}{9}-\frac{24}{3}+4=0$ $4-8+4=0$ $0=0$ The value checks and the solution set is {$\frac{2}{3}$}