Question

X-1+x(x-1)=3(x-1)

Please solve for x

Answer 1

x-1+x(x-1)=3(x-1)

x^2-1=3x-3

x^2-3x+2=0

Factor: (x-1)(x-2)=0

Set factors equal to 0:

x-1=0 and x-2=0

x=1 or x=2

Answer 2

Factor out x-1.

... (x-1)(1 + x) = 3(x-1)

... (x-1)(x +1 -3) = 0 . . . . subtract the right side

... (x -1)(x -2) = 0 . . . . . . simplify

... x = 1 . . . or . . . x = 2 . . . . use the zero-product rule*

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* A product is only zero when one or more of its factors is zero.