(8-9x)x=-40+(6-3x)(6+3x)

To solve the equation (8-9x)x=-40+(6-3x)(6+3x), we can start by expanding the right side of the equation.

(6-3x)(6+3x) = 66 + 63x - 3x6 - 3x3x = 36 + 18x - 18x - 9x^2 = 36 - 9x^2

Now, the equation becomes:

(8-9x)x = -40 + 36 - 9x^2

Next, let's combine like terms:

8x - 9x^2 = -40 - 9x^2 + 36

Simplifying further:

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

Now, we can move all the terms to one side to get a quadratic equation:

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

Simplifying:

8x = -4

Dividing both sides by 8:

x = -4/8

Simplifying further:

x = -1/2

Therefore, the solution to the equation (8-9x)x=-40+(6-3x)(6+3x) is x = -1/2.