Answer
$6x^{2}-5x+1=0$
Work Step by Step
$x=\displaystyle \frac{1}{2}$ or $ x=\displaystyle \frac{1}{3}\qquad$....get $0$'s on one side.
$x-\displaystyle \frac{1}{2}=0$ or $ x-\displaystyle \frac{1}{3}=0\qquad$....Use the principle of zero products (multiplying). The solutions of this equation are $\displaystyle \frac{1}{2}$ and $\displaystyle \frac{1}{3}$.
$(x-\displaystyle \frac{1}{2})(x-\frac{1}{3})=0\qquad$...use the FOIL method to multiply.
$ x^{2}-\displaystyle \frac{1}{3}x-\frac{1}{2}x+\frac{1}{6}=0\qquad$...combine like terms.
$ x^{2}-\displaystyle \frac{5}{6}x+\frac{1}{6}=0\qquad$...multiply both sides by $6$ to clear fractions.
$6x^{2}-5x+1=0$
