Problem: solve for x: 3x^2-5x+2=0
solve for x: 3x^2-5x+2=0
(3x - 2)(x - 1) = 0 set each factor to zero and solve for x
(3x - 2) = 0
3x = 2
x = 2/3
(x - 1) = 0
x = 1
Check.
3x^2 - 5x + 2 = 0
3(2/3)^2 - 5(2/3) + 2 = 0
3(4/9) - 10/3 + 2 = 0
4/3 - 10/3 + 2 = 0
-6/3 + 2 = 0
-2 + 2 = 0
0 = 0
3x^2 - 5x + 2 = 0
3(1)^2 - 5(1) + 2 = 0
3(1) - 5 + 2 = 0
3 - 5 + 2 = 0
0 = 0
x = 2/3 and x = 1