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