If a(b)=b^2 -2b and 4a(b)=a(2b)-24, what is the value of b?

1.5

4a(b) = a(2b)-24

4(b^2-2b) = (2b)^2-2(2b)-24
4b^2-8b = 4b^2-4b-24
4b = 24
b = 6

To find the value of b, we can substitute the given expressions into the equation and solve for b.

Given:
a(b) = b^2 - 2b
4a(b) = a(2b) - 24

Let's substitute the expression for a(b) into the second equation:

4(b^2 - 2b) = (2b)^2 - 2(2b) - 24

Simplifying the equation:

4b^2 - 8b = 4b^2 - 4b - 24

By subtracting 4b^2 from both sides and simplifying the equation further:

-8b = -4b - 24

Next, let's move all terms involving b to one side of the equation by adding 4b to both sides:

-8b + 4b = -4b + 4b - 24

-4b = -24

Finally, divide both sides of the equation by -4 to solve for b:

b = (-24) / (-4)

Simplifying the equation:

b = 6

Therefore, the value of b is 6.