Answer
$x=-4$ or $x=-\displaystyle \frac{2}{3}$
Work Step by Step
$(x+3)(3x+5)=7\qquad$...apply the FOIL method.
$ 3x^{2}+5x+9x+15=7\qquad$... add $-7$ to both sides.
$3x^{2}+14x+8=0$
... Searching for two factors of $ac=24$ whose sum is $b=14,$
we find$\qquad 12$ and $2.$
Rewrite the middle term and factor in pairs:
$3x^{2}+12x+2x+8=0$
$3x(x+4)+2(x+4)=0$
$(x+4)(3x+2)=0\qquad$...apply the principle of zero products.
$x+4=0$ or $3x+2=0$
$x=-4$ or $ 3x=-2\qquad$...divide the second expression with $3$.
$x=-4$ or $x=-\displaystyle \frac{2}{3}$
Type the equation into a graphing utility and see
that the graph intercepts the x-axis at $-4$ and $-\displaystyle \frac{2}{3}$.
