Answer
$p\approx 1.42 \quad \ \textbf{or}\ \ \ p\approx -8.42 $
Work Step by Step
First transfer the constant to the right of the equal sign proceed with completing the square in line 1 of the equation by dividing the coefficient of the $7p$ term by 2 and squaring it and adding the result on both sides.
$$
\begin{aligned}
p^2+7p -12& = 0 \\
p^2+7p & = 12 \\
p^2+7p+\left(\frac{7}{2}\right)^2 & =12+\left(\frac{7}{2}\right)^2 \\
p^2+7p+3.5^2 & =12+3.5^2 \\
(p+3.5)^2 & = 24.25
\end{aligned}
$$ Take the square root: $$
\begin{array}{rl}
(p+3.5)^2 & = 24.25 \\
p+3.5 & = \pm \sqrt{54.25} \\\\
p+3.5=\sqrt{24.25} &\ \textbf{or}\ \ \ p+3.5=-\sqrt{24.25}\\
p=-3.5+\sqrt{24.25} & \ \textbf{or}\ \ \ p= -3.5-\sqrt{24.25} \\
p\approx 1.42 & \ \textbf{or}\ \ \ p\approx -8.42
\end{array}
$$ Check $$\begin{aligned}
(-3.5+\sqrt{24.25})^2+7(-3.5+\sqrt{24.25}) -12&\stackrel{?}{=} 0 \\
0& = 0\checkmark\\
\end{aligned}$$ $$\begin{aligned}
(-3.5-\sqrt{24.25})^2+7(-3.5-\sqrt{24.25}) -12&\stackrel{?}{=} 0 \\
0& = 0\checkmark.
\end{aligned}$$ The solution is: $$p\approx 1.42 \quad \ \textbf{or}\ \ \ p\approx -8.42 $$
