Solve the following for x: (CBSE 2014)

Given: 

to find: Solution of the above quadratic equation.

Solution:

In factorization, we write the middle term of the quadratic equation either as a sum of two numbers or difference of two numbers such that the equation can be factorized.

⇒ 3(9x² + 1 – 6x) – 2(4x² + 9 + 12x) = 5(6x² – 3 + 7x)

⇒ 27x² + 3 – 18x - 8x² - 18 – 24x = 30x² - 15 + 35x

⇒ 19x² - 42x – 15 = 30x² - 15 + 35x

⇒19x² - 30x² - 42x – 35x - 15 + 15 = 0 

⇒ -11x² - 77x = 0

⇒ 11x² + 77x = 0

⇒ 11x(x + 7) = 0

⇒ x = 0, - 7