## It seems there was a mistake in the simplification of the equation. Let's go through it again step by step.

To determine if a number is positive or negative when adding, subtracting, multiplying, or dividing, you need to consider the signs involved.

For addition and subtraction:

- If two numbers have the same sign (both positive or both negative), you add their absolute values and keep the common sign.

- If two numbers have different signs, you subtract their absolute values and keep the sign of the number with the larger absolute value.

For multiplication and division:

- If two numbers have the same sign, the result is positive.

- If two numbers have different signs, the result is negative.

Now let's solve the equation -4(2x - 3) = -8x + 5 correctly:

Start by distributing -4 to the expression inside the parentheses:

-4(2x - 3) = -8x + 5

-8x + 12 = -8x + 5

Here you can see that the -8x term cancels out on both sides. So, we are left with:

12 = 5

This is a contradiction because 12 cannot be equal to 5. Therefore, the original equation -4(2x - 3) = -8x + 5 has no solution.

In general, to solve equations, simplify them step by step, combining like terms and applying the rules of arithmetic and algebra. Make sure to avoid any errors or contradictions in the calculations.