Find the roots by factoring.

25x squared - 30x= -9

25x^2 - 30x = -9

25x^2 - 30x + 9 = 0
(5x-3)(5x-3) = 0
...

anwer me pls

To find the roots by factoring, we need to rewrite the equation in standard quadratic form, which is in the format: ax^2 + bx + c = 0.

Let's start by rearranging the equation you provided:

25x^2 - 30x = -9

Now, we move all terms to one side to get the quadratic equation equal to zero:

25x^2 - 30x + 9 = 0

Since we are looking for the roots by factoring, we need to factorize the quadratic expression.

First, check if the expression can be factored further. In this case, we need to find two numbers that multiply to give 25 * 9 = 225 and add up to -30.

The factors of 225 are: 1, 3, 5, 9, 15, 25, 45, 75, and 225.

After checking, we find that -15 and -15 can be used since (-15) * (-15) = 225 and -15 + (-15) = -30.

Let's rewrite the quadratic expression with these factors:

25x^2 - 15x - 15x + 9 = 0

Now, we can group the terms:

(25x^2 - 15x) + (-15x + 9) = 0

Take out the common factors from each group:

5x(5x - 3) - 3(5x - 3) = 0

Now, notice that (5x - 3) is present in both terms. We can factor it out:

(5x - 3)(5x - 3) = 0

Since both factors are the same, we can rewrite it using exponential notation:

(5x - 3)^2 = 0

Now, set each factor equal to zero:

5x - 3 = 0

Solve for x:

5x = 3

x = 3/5

So, the equation has a repeated root at x = 3/5.