tanx(tanx+3)=18

Solution for tanx(tanx+3)=18 equation:

Simplifying
tanx(tanx + 3) = 18

Reorder the terms:
antx(3 + antx) = 18
(3 * antx + antx * antx) = 18
(3antx + a2n2t2x2) = 18

Solving
3antx + a2n2t2x2 = 18

Solving for variable 'a'.

Reorder the terms:
-18 + 3antx + a2n2t2x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 3antx + a2n2t2x2 = 0

Factor a trinomial.
(-6 + -1antx)(3 + -1antx) = 0

Subproblem 1
Set the factor '(-6 + -1antx)' equal to zero and attempt to solve:

Simplifying
-6 + -1antx = 0

Solving
-6 + -1antx = 0

Move all terms containing a to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + -1antx = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1antx = 0 + 6
-1antx = 0 + 6

Combine like terms: 0 + 6 = 6
-1antx = 6

Divide each side by '-1ntx'.
a = -6n-1t-1x-1

Simplifying
a = -6n-1t-1x-1
Subproblem 2
Set the factor '(3 + -1antx)' equal to zero and attempt to solve:

Simplifying
3 + -1antx = 0

Solving
3 + -1antx = 0

Move all terms containing a to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1antx = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1antx = 0 + -3
-1antx = 0 + -3

Combine like terms: 0 + -3 = -3
-1antx = -3

Divide each side by '-1ntx'.
a = 3n-1t-1x-1

Simplifying
a = 3n-1t-1x-1
Solution
a = {-6n-1t-1x-1, 3n-1t-1x-1}