Final answer:
To find the solutions for the equation 3x²-12x-15, factor out the greatest common factor (GCF) and then solve the resulting quadratic equation.
Step-by-step explanation:
To find the solutions for the equation 3x²-12x-15, we can start by factoring out the greatest common factor (GCF), if it exists. In this case, the GCF is 3.
So, we can rewrite the equation as 3(x²-4x-5).
Now, we can solve the quadratic equation x²-4x-5=0 by factoring or using the quadratic formula.
By factoring, we can split the middle term -4x into two terms that when multiplied give -5x, and when added give -4x. The factors are (x-5) and (x+1).
Therefore, the solutions to the equation 3x²-12x-15=0 are x=5 and x=-1.