Answer:
a = - 2 , a = 6
Explanation:
a² - 4a - 12 = 0
consider the factors of the constant term (- 12) which sum to give the coefficient of the a- term (- 4)
the factors are + 2 and - 6, since
+ 2 × - 6 = - 12 and + 2 - 6 = - 4
use these factors to split the a- term
a² + 2a - 6a - 12 = 0 ( factor the first/second and third/fourth terms )
a(a + 2) - 6(a + 2) = 0 ← factor out common factor (a + 2) from each term
(a + 2)(a - 6) = 0 ← in factored form
equate each factor to zero and solve for a
a + 2 = 0 ( subtract 2 from each side )
a = - 2
a - 6 = 0 ( add 6 to both sides )
a = 6
solutions are a = - 2 , a = 6