5z ^ 2 - 20z + 25 = z ^ 2

To solve the equation, we need to isolate the variable on one side of the equation. Let's subtract z^2 from both sides:

5z^2 - 20z + 25 - z^2 = 0

This simplifies to:

4z^2 - 20z + 25 = 0

Now, let's see if we can factor the left side of the equation. The factors of 4z^2 are (2z)(2z) or (4z)(z). The factors of 25 are (5)(5). So, we have:

(2z - 5)(2z - 5) = 0

We can rewrite this as:

(2z - 5)^2 = 0

To find the value of z, we set the squared factor equal to zero:

2z - 5 = 0

Adding 5 to both sides of the equation:

2z = 5

Finally, dividing both sides by 2:

z = 5/2 or z = 2.5

Therefore, the solutions to the equation are z = 5/2 or z = 2.5.