Answer
$r=1,-7$
Work Step by Step
$3r^2+18r=21$
Re-write the equations as: $r^2+6r=7$
Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=6$
Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$
Thus, $c=\dfrac{b^2}{4a}=\dfrac{(6)^2}{4}=9$
To complete the square, add $9$ on both sides.
$r^2+6r+9=7+9$
$\implies (r+3)^2=16$
$\implies r+3=4$
and
$\implies r+3=-4$
or, $r=1,-7$
