Solve each of the following equations using the Principle of Zero Products and match it to its correct pair of solutions on the right. Each pair on the right will be used once. (x-6)(3x+1)=0 (x+6)(x+3)=0 (x+6)(3x-1)=0 (x-6)(x-3)=0 x=-6 or x=(1)/(3) x=6 or x=-(1)/(3) x=-6 or x=-3 x=6 or x=3

To solve each equation using the Principle of Zero Products, we need to set each factor equal to zero and solve for x.<br /><br />1. $(x-6)(3x+1)=0$<br /> - Set each factor equal to zero:<br /> $x-6=0$ or $3x+1=0$<br /> - Solve for x:<br /> $x=6$ or $x=-\frac{1}{3}$<br /><br />2. $(x+6)(x+3)=0$<br /> - Set each factor equal to zero:<br /> $x+6=0$ or $x+3=0$<br /> - Solve for x:<br /> $x=-6$ or $x=-3$<br /><br />3. $(x+6)(3x-1)=0$<br /> - Set each factor equal to zero:<br /> $x+6=0$ or $3x-1=0$<br /> - Solve for x:<br /> $x=-6$ or $x=\frac{1}{3}$<br /><br />4. $(x-6)(x-3)=0$<br /> - Set each factor equal to zero:<br /> $x-6=0$ or $x-3=0$<br /> - Solve for x:<br /> $x=6$ or $x=3$<br /><br />Now, let's match each equation to its correct pair of solutions:<br /><br />1. $(x-6)(3x+1)=0$ matches with $x=6$ or $x=-\frac{1}{3}$<br />2. $(x+6)(x+3)=0$ matches with $x=-6$ or $x=-3$<br />3. $(x+6)(3x-1)=0$ matches with $x=-6$ or $x=\frac{1}{3}$<br />4. $(x-6)(x-3)=0$ matches with $x=6$ or $x=3$