Question

Solve the following quadratic equations by factorization method.

Answer 1

3(x - 4)² - 5(x - 4) = 12
For better understanding , let (x - 4) = P
then, equation converts into 3P² - 5P = 12
⇒3P² - 5P - 12 = 0
⇒3P² - 9P + 4P - 12 = 0
⇒3P(P - 3) + 4(P - 3) = 0
⇒(3P + 4)(P - 3) = 0

Now, put P = (x - 4)
⇒{3(x - 4) + 4}{(x - 4) - 3} = 0
⇒{3x - 8}{x - 7} = 0
⇒3x - 8 = 0 and (x - 7) = 0
x = 8/3 and x = 7

Hence, x = 8/3 , 7

Answer 2

3(x - 4)² - 5(x - 4) = 12
3(x² - 16 - 8x) - 5x + 20 = 12
3x² - 48 - 24x - 5x + 20 = 12
3x² - 29x + 56 = 0
3x² - 21x - 8x + 56 = 0
3x(x - 7) - 8(x - 7) = 0
(3x - 8)(x - 7) = 0
x = 7 , x = 8/3