Tan^2x+5cotx+7=0

To solve the equation tan^2(x) + 5cot(x) + 7 = 0, we can use the identity cot(x) = 1/tan(x).

Let's substitute cot(x) with 1/tan(x):

tan^2(x) + 5(1/tan(x)) + 7 = 0

Now, let's multiply the entire equation by tan(x) to get rid of the denominators:

tan^3(x) + 5 + 7tan(x) = 0

Rearranging the equation:

tan^3(x) + 7tan(x) + 5 = 0

Now, let's substitute tan(x) with y:

y^3 + 7y + 5 = 0

Unfortunately, this equation does not have a simple algebraic solution. You can solve it numerically using methods such as Newton's method or graphing the equation to find the approximate solutions.