Answer
$p=2\pm\sqrt{\dfrac{10}{3}}$
Work Step by Step
$3p^{2}-12p+2=0$
Take the $2$ to substract to the right side of the equation:
$3p^{2}-12p=-2$
Take out common factor $3$ from the left side of the equation:
$3(p^{2}-4p)=-2$
Add $\Big(\dfrac{b}{2}\Big)^{2}$ to the expression inside the parentheses and $3\Big(\dfrac{b}{2}\Big)^{2}$ to the right side of the equation. For this case, $b=-4$
$3\Big[p^{2}-4p+\Big(\dfrac{-4}{2}\Big)^{2}\Big]=-2+3\Big(\dfrac{-4}{2}\Big)^{2}$
$3(p^{2}-4p+4)=-2+12$
$3(p^{2}-4p+4)=10$
Now, factor the expression inside the parentheses, which is a perfect square trinomial:
$3(p-2)^{2}=10$
Take the $3$ to divide to the right side of the equation:
$(p-2)^{2}=\dfrac{10}{3}$
Take the square root of both sides of the equation:
$\sqrt{(p-2)^{2}}=\pm\sqrt{\dfrac{10}{3}}$
$p-2=\pm\sqrt{\dfrac{10}{3}}$
Solve for $p$:
$p=2\pm\sqrt{\dfrac{10}{3}}$
