6t2 - t - 1 = 0
One approach to solving this equation is to factor by grouping.
Step 1: multiply the leading coefficient, 6, by the constant term, -1 to get -6.
Step 2: find two numbers whose product is -6(the result of step 1) and whose sum is -1(the coefficient of the middle term. It's easy to see that the numbers are -3 and 2.
Step 3: rewrite the middle term as -3t + 2t and factor by grouping:
6t2 - t - 1 = 0
6t2 - 3t + 2t - 1 = 0
3t(2t - 1) +1(2t - 1) = 0
(2t - 1)(3t + 1) = 0
2t - 1 = 0 or 3t + 1 = 0
2t = 1 or 3t = -1
t = 1/2, -1/3
