$ (2 x-3)(x-5)=(x-3)^{2} $

Given: (2x - 3)(x - 5) = (x - 3)² 

To find: We have to find the value of x.

Solution: 

(2x - 3)(x - 5) = (x - 3)²  

2x(x - 5)  - 3(x - 5) = x² + 9 - 6x 

2x² - 10x  - 3x + 15 = x² + 9 - 6x 

2x² - x² - 13x + 6x + 15 - 9 = 0 

x² - 7x + 6 = 0 

x² - 6x - x + 6 = 0 

x(x - 6) - (x - 6) = 0 

(x - 6)(x - 1) = 0 

Now,

x - 6 = 0

x = 6

Also,

x - 1 = 0

x = 1

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Updated on: 10-Oct-2022

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