To solve the equation 3x^2 - 7x + 5 = 1 by trinomial factoring, we need to rewrite it in the form of (ax + b)(cx + d) = 0.
First, we move the constant term to the left-hand side of the equation:
3x^2 - 7x + 4 = 0
Next, we need to find two numbers whose product is 3 times 4 = 12 and whose sum is -7. These numbers are -3 and -4.
We can use these numbers to factor the expression as follows:
3x^2 - 7x + 4 = (3x - 4)(x - 1)
Therefore, the solutions to the original equation are:
3x - 4 = 0, which gives x = 4/3
x - 1 = 0, which gives x = 1
So the solution set is {4/3, 1}.