To factor the left hand side of the equation, let's first put it in standard form:
7x^2 - 15x + 2 = 0
To factor this quadratic equation, we need to find two numbers whose product is equal to the product of the coefficient of the x^2 term (7) and the constant term (2), and whose sum is equal to the coefficient of the x term (-15).
The product of 7 and 2 is 14, so we need to find two numbers that multiply to 14 and add up to -15. The numbers that fit this criteria are -14 and -1.
Now let's rewrite the middle term (-15x) as the sum of -14x and -x:
7x^2 - 14x - x + 2 = 0
Group the terms:
(7x^2 - 14x) + (-x + 2) = 0
Factor out the greatest common factor in each group:
7x(x - 2) - 1(x - 2) = 0
Now we can see that we have a common factor of (x - 2) in both terms. Factor out the common factor:
(x - 2)(7x - 1) = 0
So the left hand side of the equation factors into (x - 2)(7x - 1).