Factor the trinomial. \[ 15 t^{2}+39 t-18 \]

Step 1 ：Multiply the coefficient of the quadratic term (15) by the constant term (-18): \(15 \times -18 = -270\)

Step 2 ：Find two numbers that multiply to give -270 and add up to the coefficient of the linear term (39): 45 and -6

Step 3 ：Rewrite the middle term (39t) using the two numbers found in step 2: \(15t^2 + 45t - 6t - 18\)

Step 4 ：Group the terms and factor by grouping: \(15t(t + 3) - 6(t + 3)\)

Step 5 ：Factor out the common binomial factor: \((t + 3)(15t - 6)\)