To solve for x in this equation, we must first perform the operations inside the parentheses. This gives us:
X = 40 * (25x^2 + 75x + 75x - 75)
Next, we can distribute the 40 and combine like terms to get:
X = 1000x^2 + 3000x - 3000
Now, we can set this expression equal to X and solve for x.
1000x^2 + 3000x - 3000 = X
We can use the quadratic formula to find the solutions for x:
x = (-3000 +/- sqrt(3000^2 - 4 * 1000 * (-3000))) / (2 * 1000)
This simplifies to:
x = (-3000 +/- sqrt(9000000 + 24000000)) / 2000
Finally, we can simplify further to get:
x = (-3000 +/- sqrt(33000000)) / 2000
Thus, the solutions for x are:
x = (-3000 + sqrt(33000000)) / 2000
x = (-3000 - sqrt(33000000)) / 2000
These are the possible values for x that satisfy the given equation.