Answer:
x = 4, x = 8
Step-by-step explanation:
To find the roots equate to zero, that is
- x² + 12x - 32 = 0 ( multiply through by - 1 )
x² - 12x + 32 = 0
Consider the factors of the constant term (+ 32) which sum to give the coefficient of the x- term (- 12)
The factors are - 4 and - 8, since
- 4 × - 8 = + 32 and - 4 - 8 = - 12, thus
(x - 4)(x - 8) = 0
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x - 8 = 0 ⇒ x = 8
