Solve for x : 4x2 - 4ax + (a2-b2) = 0

Problem : Solve the quadratic equation: 4x² - 4ax + (a²-b²) = 0 by factorisation method.

Doubt by Sanya (Added on 15/02/2020)
 
Problem : Solve for x : 4x² - 4ax + (a²-b²) = 0

Doubt by Muskan (Added on 29/07/2020)

Solution : 

4x² - 4ax + (a²-b²) = 0
4x² - 4ax + (a+b)(a-b) = 0
4x² - [2(a+b) + 2 (a-b)]x + (a+b)(a-b) = 0
4x² - 2(a+b)x - 2(a-b)x + (a+b)(a-b) = 0
2x [2x - (a+b)] - (a-b) [ 2x - (a+b)] = 0
[2x - (a-b)] [2x - (a+b)] = 0

2x - (a-b) = 0
2x = (a-b)
x = (a-b)/2

OR

2x - (a+b) = 0
2x = (a+b)
x = (a+b)/2

∴ x = (a-b)/2, (a+b)/2