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

which is equivalent to:

4x^2-8x+3x-9=-3

which further simplifies to:

4x^2-5x-9=-3

We want all the terms to one side:

4x^2-5x-6=0 or 0=4x^2-5x-6=0

We can first attempt to factor terms, since this will obviate the need for the Quadratic Formula:

(4x+3)(x-2)=0

This works for us. Multiply through:

4x^2-8x+3x-6= 4x^2-5x-6=0

So our answers are:

x=2 (from the term (x-2)

and 4x+3=0, x=-3/4

so the answer is x= 2, -3/4

4(x-2)/(x-3) + 3/x + 3/x(x-3) = 0

4(x-2)/(x-3) + (3/x)[(x-3)/(x-3)] + 3/x(x-3) = 0

[1/(x-3)] [4(x-2) + (3/x)(x-3) + 3/x] = 0

[4(x-2) + (3/x)(x-3) + 3/x] = 0

4(x-2)(x/x) + (3/x)(x-3) + 3/x = 0

(1/x)[4(x-2)x + 3(x -3) + 3] = 0

[4(x-2)x + 3(x -3) + 3] = 0

4x^2 – 8x + 3x – 9 + 3 = 0

4x^2 – 5x – 6 = 0

I think I did the brackets properly

but i’m the forward slashes where confussing