What is the solution set of (x - 2)(x - 3) = 2? a. {1, 4} b. {2, 3} c. {4, 5}

Step One
Remove the brackets. Use Foil
F: x^2
O: -3x
I: -2x
L:(-2)(-3) = 6

What you have now is
x^2 - 3x - 2x + 6 = 2

Step Two
Combine like terms.
x^2 - 5x + 6 = 2

Step Three
Subtract 2 from both sides.
x^2 - 5x + 6 - 2 = 0
x^2 - 5x + 4 = 0

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

Step 5
Find the zeros.
x - 4 = 0
x = 4

x -1 = 0
x = 1

Solution Set
(1,4)