Answer:
x = {1/2, 5/3}
Explanation:
You want to solve 6x^2-13x+5=0 by factoring.
Factors
As an aid to finding the polynomial factors, you want the factors of (6)(5) = 30 that have a total of -13.
30 = (-1)(-30) = (-2)(-15) = (-3)(-10) = (-5)(-6)
The sums of these factor pairs are -31, -17, -13, -11. The pair of interest is (-3)(-10), with a sum of -13.
We can use these numbers to rewrite the linear term, then factor by grouping.
6x^2 -3x -10x +5 = 0 . . . . split the middle term
(6x^2 -3x) -(10x -5) = 0 . . . . . group pairs of terms
3x(2x -1) -5(2x -1) = 0 . . . . . . . . factor each pair
(3x -5)(2x -1) = 0 . . . . . . . . the factored quadratic equation
Solutions
The solutions to the equation are the values of x that make the factors zero:
(3x -5) = 0 ⇒ x = 5/3
(2x -1) = 0 ⇒ x = 1/2