To find the value of L when a = 7 and c = 9, we substitute these values into the given expression:
L = 36a(a-c) - 24c(2a-3c) + 2a(-2(3a+c)) + 77
First, let's substitute the values for a and c:
L = 36(7)(7-9) - 24(9)(2(7)-3(9)) + 2(7)(-2(3(7)+9)) + 77
Simplifying the expression inside the parentheses:
L = 36(7)(-2) - 24(9)(14-27) + 2(7)(-2(21+9)) + 77
L = 36(7)(-2) - 24(9)(-13) + 2(7)(-2(30)) + 77
Now, let's simplify the multiplications:
L = -504 - (-2808) + (-84)(-60) + 77
L = -504 + 2808 + 5040 + 77
Finally, let's add the numbers together:
L = 3900
Therefore, when a = 7 and c = 9, the value of L is 3900.