Simplify and show:

2a-6(10a)-5a^2(2)
-----------------
(2a-6)^2

This is my work but its not right.

10a-10a^2
--------
2a-6

Then solve for a by setting numerator to zero. so I got this...

10a-10a^2=0
10a(1-a)=0
a=0, a=1

My book says a=0, or a=6 why didn't I get this?

To simplify the expression and find the correct values of "a," you need to reevaluate your calculations. Let's go through the steps together.

Step 1: Simplify the numerator.
The numerator is 2a - 6(10a) - 5a^2(2). Start by applying the distributive property:
2a - 60a - 10a^2.

Combine like terms:
-58a - 10a^2.

Step 2: Simplify the denominator.
The denominator is (2a - 6)^2.

Expand the square:
(2a - 6)(2a - 6) = 4a^2 - 12a - 12a + 36.

Combine like terms:
4a^2 - 24a + 36.

So the expression becomes:
(-58a - 10a^2) / (4a^2 - 24a + 36).

Step 3: Factorize the numerator and denominator (if possible).
Let's factor the numerator first:
-2a(29 + 5a).

The denominator is already factored: (2a - 6)(2a - 6).

Now the expression becomes:
(-2a(29 + 5a)) / ((2a - 6)(2a - 6)).

Step 4: Cancel out common factors.
We can cancel out the common factor of (2a - 6) in the numerator and the denominator:
(-2a(29 + 5a)) / (2a - 6).

Step 5: Set the numerator equal to zero and solve for "a."
(-2a(29 + 5a)) = 0.

To find the values of "a," we set each factor equal to zero:
-2a = 0 (Equation 1) and (29 + 5a) = 0 (Equation 2).

Solve Equation 1:
-2a = 0.

Divide both sides by -2 to isolate "a":
a = 0.

Solve Equation 2:
29 + 5a = 0.

Subtract 29 from both sides to isolate "a":
5a = -29.

Divide both sides by 5:
a = -29/5.

Therefore, the possible values for "a" are a = 0 and a = -29/5, which is equivalent to a = -5.8.

It seems that in your calculations, you had a mistake when simplifying the numerator and finding the correct factors. Double check your work to ensure accuracy.