I need to find the value of x.

9x^3 + 9x = 30x^2
It's confusing because apparently I have to do 9x^3 + 9x and then add the + 30x^2 to it, and then make it equal 0, so it ends up like this:

9x^3 + 9x + 30x^2 = 0
And afterward, I would factor it. How do you factor it?
I'm having trouble factoring in general. =/

9x^3 + 9x + 30x^2 =

x [9 x^2 + 30 x + 9]

Then x = 0 or 9 x^2 + 30 x + 9 = 0

Divide by 3:

3 x^2 + 10 x + 3 = 0

(3 x + 1)(x + 3) = 0

x = -3 or x = -1/3

9x^3 + 9x = 30x^2

AFTER SUBTRACTING 30X^2 FROM EACH SIDE SHOULD BE LIKE SO;

9x^3 + 9x -30^2 = 0

IS THIS THE PROBLEM?

x^2+3x-18=0

To solve the equation 9x^3 + 9x + 30x^2 = 0, you are correct in first setting it equal to zero:

9x^3 + 9x + 30x^2 = 0

Factoring a polynomial involves finding its factors or expressions that can multiply together to give you the original polynomial.

In this case, let's try factoring by grouping.

First, let's factor out the greatest common factor, which is 3x:

3x(3x^2 + 3 + 10x)

Now, let's focus on factoring the quadratic expression (3x^2 + 3 + 10x) by grouping.

Split the middle term, 10x, into two terms such that their coefficients multiply to give you the product of the coefficient of the squared term (3x^2) and the constant term (3). In this case, we need to split 10x into 9x and 1x:

3x(3x^2 + 9x + x + 3)

Now, the expression can be rearranged by grouping terms:

3x((3x^2 + 9x) + (x + 3))

Next, factor out the greatest common factor from each group of terms:

3x(3x(x + 3) + (x + 3))

Notice that there is a common binomial factor of (x + 3):

3x(x + 3)(3x + 1)

Now, we have factored the original equation. The solutions to the equation would be values of x that make any of these factors (3x, x + 3, 3x + 1) equal to zero.