How do I solve (x-2)(x-3)=2?

Question

please show steps :)

Answer 1

Given (x - 2)(x - 3) = 2.

(x - 2)(x - 3) - 2 = 0

By foil method : (a + b)(c + d) = ac + ad + bc + bd.

x^2 - 2x - 3x + 6 - 2 = 0

x^2 - 5x + 4 = 0

By factor by grouping.

x^2 - 4x - x + 4 = 0

x(x - 4) - 1(x - 4) = 0

Factor : (x - 4)(x - 1) = 0.

Apply zero product property.

x - 4 = 0 and x - 1 = 0

x = 4 and x  =  1.

Solution is x = 4 and x =  1.