Factor 3g^2-42y+144

To factor the expression 3g^2 - 42y + 144, we can look for common factors first, then use the quadratic formula if necessary.

First, check if there is a common factor. In this case, there is a common factor of 3.
3g^2 - 42y + 144 = 3(g^2 - 14y + 48)

Next, we need to factor the quadratic expression inside the parentheses, g^2 - 14y + 48:
For this expression, we are looking for two numbers that multiply to 48 and add up to -14. The numbers are -6 and -8.
Therefore, the quadratic expression factors to:
g^2 - 14y + 48 = (g - 6)(g - 8)

Finally, we substitute this result back into the original expression:
3(g^2 - 14y + 48) = 3(g - 6)(g - 8)

So, the factored form of 3g^2 - 42y + 144 is 3(g - 6)(g - 8).