Answer:
p = - 6, p = - 2
Step-by-step explanation:
Given
- 2p² = 16p + 24
Subtract 16p + 24 from both sides
- 2p² - 16p - 24 = 0 ← in standard form ( divide all terms by - 2)
p² + 8p + 12 = 0
To factor the quadratic
Consider the factors of the constant term (+ 12) which sum to give the coefficient of the p- term (+ 8)
The factors are + 6 and + 2, since
6 × 2 = 12 and 6 + 2 = 8, thus
(p + 6)(p + 2) = 0
Equate each factor to zero and solve for p
p + 6 = 0 ⇒ p = - 6
p + 2 = 0 ⇒ p = - 2
