Bonjour,
On commence par simplifier A(x)
A(x) =5(x-2)²-2(x-2)(x+1) = (x-2) (5 (x-2) - 2 (x+1)
A(x) = (x-2) (5x - 10 - 2x -2)
A(x) = (x-2) (3x -12)
A(x) = 3 (x-2) (x - 4)
A(x) = 3 (x² - 6x + 8)
A(x) = 24 ⇔ 3 (x² - 6x + 8) = 3 * 8
⇔ x² - 6x + 8 = 8
⇔ x² - 6x = 0
⇔ x (x - 6) = 0
⇔ x = 0 ou x - 6 = 0
⇔ x = 0 ou x = 6
