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

To solve the equation (8-9x)x = -40 + (6-3x)(6+3x), we will first simplify the equation and then use the distributive property to expand the expressions in the parentheses.

Step 1: Distribute (6-3x)(6+3x): (6-3x)(6+3x) = 6(6) + 6(3x) - 3x(6) - 3x(3x) = 36 + 18x - 18x - 9x^2 = 36 - 9x^2

Step 2: Rewrite the equation: (8-9x)x = -40 + 36 - 9x^2

Step 3: Simplify the equation further: 8x - 9x^2 = -4 - 9x^2

Step 4: Subtract (-9x^2) from both sides of the equation: 8x - 9x^2 + 9x^2 = -4 - 9x^2 + 9x^2 8x = -4

Step 5: Divide both sides of the equation by 8: 8x/8 = -4/8 x = -1/2

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