# Appendix A - Equations and Inequalities - Page 420: 36

{$-\frac{5}{6},2$}

#### Work Step by Step

$-6x^{2}+7x=-10$ Adding 10 on both sides, $-6x^{2}+7x+10=-10+10$ Simplifying, $-6x^{2}+7x+10=0$ $6x^{2}-7x-10=0$ $6x^{2}-12x+5x-10=0$ $6x(x-2)+5(x-2)=0$ $(x-2)(6x+5)=0$ $(x-2)=0$ or $(6x+5)=0$ $x=2$ or $x=-\frac{5}{6}$ Check: Substituting $x=2$ in the equation, $6(2)^{2}-7(2)-10=0$ $24-14-10=0$ $24-24=0$ $0=0$ Substituting $x=-\frac{5}{6}$ in the equation, $6(-\frac{5}{6})^{2}-7(-\frac{5}{6})-10=0$ $\frac{6\times25}{36}+\frac{35}{6}-10=0$ $\frac{25}{6}+\frac{35}{6}-10=0$ $\frac{60}{6}-10=0$ $10-10=0$ $0=0$ Both values check and the solution set is {$-\frac{5}{6},2$}

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