To solve this equation, we can start by expanding the left side:
(x+1)(x+2)(x+4)(x+5)= (x^2 + 3x + 2)(x^2 + 9x + 20)= x^4 + 9x^3 + 20x^2 + 3x^3 + 27x^2 + 60x + 2x^2 + 18x + 40= x^4 + 12x^3 + 49x^2 + 78x + 40
Now we can set this equal to 40 and solve for x:
x^4 + 12x^3 + 49x^2 + 78x + 40 = 40x^4 + 12x^3 + 49x^2 + 78x = 0
We can see that x = 0 is a solution. Now we can use polynomial division or factoring to find the remaining solutions.
To solve this equation, we can start by expanding the left side:
(x+1)(x+2)(x+4)(x+5)
= (x^2 + 3x + 2)(x^2 + 9x + 20)
= x^4 + 9x^3 + 20x^2 + 3x^3 + 27x^2 + 60x + 2x^2 + 18x + 40
= x^4 + 12x^3 + 49x^2 + 78x + 40
Now we can set this equal to 40 and solve for x:
x^4 + 12x^3 + 49x^2 + 78x + 40 = 40
x^4 + 12x^3 + 49x^2 + 78x = 0
We can see that x = 0 is a solution. Now we can use polynomial division or factoring to find the remaining solutions.