Factor Completelyminus, 20, z, squared, plus, 44, z, plus, 48−20z 2 +44z+48

To factor the quadratic equation -20z^2 + 44z + 48 completely, follow these steps:

Step 1: Factor out the greatest common factor (GCF) if there is one. In this case, the GCF is 4. So, we get:

4(-5z^2 + 11z + 12)

Step 2: Now, we need to factor the quadratic equation -5z^2 + 11z + 12. We are looking for two numbers that multiply to (a*c) -60 (a is the coefficient of z^2 and c is the constant term) and add up to b, which is 11. Those numbers are -4 and 15.

Step 3: Rewrite the middle term (11z) as the sum of -4z and 15z:

4[-5z^2 -4z + 15z + 12]

Step 4: Group the terms and factor by grouping:

4[(-5z^2 -4z) + (15z + 12)]

4[z(-5z -4) + 3(5z + 4)]

Step 5: Notice that (-5z -4) is a common factor. Factor that out to get the final answer:

4(-5z -4)(z + 3)

So, the completely factored form of -20z^2 + 44z + 48 is 4(-5z -4)(z + 3).