What is are the steps to factoring -x^2 + 6x -9

Step-by-step explanation:

-x^2 + 6x - 9

The first step is to find the coefficient of x^2 (i.e. the num in front of x^2) = -1

The constant is -9

Therefore, the product of the equation = -1 x -9 = +9

Sum of the equation = the coefficient of x = +6

Then, we look for two factors (numbers) whose product = +9, and sum = +6

What of +3 and +3 ?

+3 +3 = +6

+3 x +3 = +9

Therefore, +3 and +3 are the factors of the equation.

We then substitute the sum of the equation (+6x) with these factors.

So, we have,

-x^2 + 3x +3x - 9

We then pair the equation and equate to Zero

(-x^2 + 3x) (+3x - 9) = 0

Common factor in the first pair is -x and +3 in the second.

-x(x - 3) +3 (x - 3) = 0

At this stage, same factor must be in the bracket (i.e. x-3)

So, we now have,

(-x +3) (x-3) = 0

We equate each to zero

-x + 3 = 0 and x-3=0

-x = - 3. and x = +3

x = +3 and x = +3

Therefore, x = +3 and +3

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step-by-step explanation: