is -2x+3 same as 2x-3?

-2x + 3 is not exactly the same as 2x - 3

You said it yourself, -2x + 3 times by -1 is 2x - 3. Hence they are not identical.

-2x + 3 = 0
2x - 3 = 0

These are equivalent statements, but all this actually tells us is that the solution x for both equations is the same.

If we had had
-2x + 3 = 2
then
2x - 3 = -2

They are not equal in this case.

Try plotting y = 2x - 3 and y = -2x + 3. They cross the x-axis at the same place, but are otherwise not equal (they are mirror images, reflected in the x-axis)

No. -2x + 3 =/= 2x - 3 for all real x, and you answered your own question in so doing.

-2x + 3 = -1(2x - 3), and dividing both sides by 2x - 3 means -1 = 1. False statement for all x except if x = 3/2.

if they were the same, then they would be equal for any value of x, but they are not equal at x=0

No.

Let x = 0

-2(0) + 3 = 3

2(0)- 3 = - 3

Do you see that the answers are different?

I had been taught not to leave a negative answer, so -2x + 3 would be 2x - 3. Was I taught wrong?

Let's say -2x + 3 is equal to a number a

-2x + 3 = a

Multiplying both sides by -1,

2x - 3 = -a ............(1)

However, -a ≠ a.
Take any number for a. Let's say a = 2.
2 and -2 are not the same.

Therefore -2x + 3 and 2x - 3 are not equal. You could even test them by plugging in real numbers for x.
Let x = 1,
-2x + 3 = -2(1) + 3
= -2 + 3
= 1

If x = 1 for 2x - 3,
2(1) - 3 = 2 - 3
= -1

-1 and 1 are not equal!

In a word_______ NO !!!!

- 2x + 3 = - ( 2x - 3 )

-2x+3 is not the same thing as 2x-3
It is the negative of the first expression, as you said.
-2x+3 = 0 is the same as 2x-3 = 0
Don't confuse a polynomial expression with an equation.

Test them for x=0.

What if they don't equal 0?
Let x = 1.
-2(1) + 3 = 1
but
2(1) - 3 = -1
Therefore, the expressions are not equal.