Question 290119
First let's convert {{{ 3p^2 = -13p -12 }}} to a quadratic, 
in the form of {{{ ax^2 + bx + c = 0 }}} so:
{{{ 3p^2 = highlight(-13p -12) }}} becomes:
{{{ 3p^2 + highlight( 13p + 12) = 0 }}} <br>
Now plug those numbers into the quadratic formula, 
replacing a b & c as above:
 {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}<br>
a = 3
b = 13
c = 12
Replacing "x" with "p" {{{highlight(x) = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} Becomes {{{highlight(p) = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}<br>

Replacing "a" with "3" {{{p = (-b +- sqrt( b^2-4*highlight(a)*c ))/(2*highlight(a)) }}} becomes {{{p = (-b +- sqrt( b^2-4*highlight(3)*c ))/(2*highlight(3)) }}}<br>

Replacing "b" with "13" {{{p = (-highlight(b) +- sqrt( highlight(b)^2-4*3*c ))/(2*3) }}} becomes {{{p = (-highlight(13) +- sqrt( highlight(13)^2-4*3*c ))/(2*3) }}}<br>

Replacing "c" with "12" {{{p = (-13 +- sqrt( 13^2-4*3*highlight(c) ))/(2*3) }}} becomes {{{p = (-13 +- sqrt( 13^2-4*3*highlight(12) ))/(2*3) }}}<br>
Mr. Ichudov's Quadratic Solver explains the remaining process better than I:
*[invoke quadratic "p", 3, 13, 12]
So your solutions are: p=-1.33333333333333 and p=-3. and bob's your uncle!