Réponse :

Explications étape par étape

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Factoriser :

f(x) = (2x - 6)(-12x + 20) + 4(x - 3)(10x - 12)

f(x) = 2(x - 3) * 4(-3x + 5) + 4(x - 3) * 2(5x - 6)

f(x) = 8(x - 3)(-3x + 5 + 5x - 6)

f(x) = 8(x - 3)(2x - 1)

Developper :

f(x) = 8(2x^2 - x - 6x + 3)

f(x) = 8(2x^2 - 7x + 3)

f(x) = 16x^2 - 56x + 24

f(x) = 0 ; f(x) = 24 ; f(x) = 11

8(x - 3)(2x - 1) = 0

x - 3 = 0 ou 2x - 1 = 0

x = 3 ou 2x = 1

x = 3 ou x = 1/2

16x^2 - 56x + 24 = 24

16x^2 - 56x = 24 - 24

8x(2x - 7) = 0

8x = 0 ou 2x - 7 = 0

x = 0 ou 2x = 7

x = 0 ou x = 7/2

16x^2 - 56x + 24 = 11

16x^2 - 56x + 24 - 11 = 0

16x^2 - 56x + 13 = 0

(4x)^2 - 2 * 4x * 7 + 7^2 - 7^2 + 13 = 0

(4x - 7)^2 - 49 + 13 = 0

(4x - 7)^2 - 36 = 0

(4x - 7)^2 - 6^2 = 0

(4x - 7 - 6)(4x - 7 + 6) = 0

(4x - 13)(4x + 1) = 0

4x - 13 = 0 ou 4x + 1 = 0

4x = 13 ou 4x = -1

x = 13/4 ou x = -1/4