Answer:
p is approximately equal to 1.125, -1.925
Explanation:
We can solve this first by expanding, giving us a quadratic equation in the usual ax² + bx + c format, then solving that for p:
(4p - 4)(13p + 27) = 0
52p² + 108p - 52p - 108 = 0
52p² + 52p - 108 = 0
13p² + 13p - 27 = 0
13p² + 13p = 27
p² + p = 27 / 13
p² + p + 1/4 = 27/13 + 1/4
(p + 1/2)² = 108 / 52 + 13 / 52
(p + 1/2)² = 121 / 52
p + 1/2 = ± √(121 / 52)
p = -1/2 ± 11√(1/13) / 2
At that point we can simply plug those numbers into a calculator and solve it:
p ≈ 1.125, -1.925