Answer
$8x^{2}+6x+1=0$
Work Step by Step
$x=-\displaystyle \frac{1}{4}$ or $ x=-\displaystyle \frac{1}{2}\qquad$....get $0$'s on one side.
$x+\displaystyle \frac{1}{4}=0$ or $ x+\displaystyle \frac{1}{2}=0\qquad$....Use the principle of zero products (multiplying). The solutions of this equation are $-\displaystyle \frac{1}{4}$ and $-\displaystyle \frac{1}{2}$.
$(x+\displaystyle \frac{1}{4})(x+\frac{1}{2})=0\qquad$...use the FOIL method to multiply.
$ x^{2}+\displaystyle \frac{1}{2}x+\frac{1}{4}x+\frac{1}{8}=0\qquad$...combine like terms.
$ x^{2}+\displaystyle \frac{3}{4}x+\frac{1}{8}=0\qquad$...multiply both sides by $8$ to clear fractions.
$8x^{2}+6x+1=0$
