Question

How to factor 2c^2-7c+3

Answer 1

(c - 3)(2c - 1) is the factored form

Answer 2

$2c^2-7c+3$

You need 2 numbers that when added together equal the coefficient of c (-7 in this case), and when multiplied equal the product of the constant and coefficient of c^2 (this product is 2*3 = 6).
Two numbers that add to -7 and multiply to 6 are -6 and -1.

The middle term -7c becomes -6c - 1c.
$2c^2-6c-1c+3 \\ 2c(c-3) -1(c-3) \\ (c-3)(2c-1)$