tan(3x-20)=cot(x+18)

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Solution for tan(3x-20)=cot(x+18) equation: 


Simplifying
tan(3x + -20) = cot(x + 18)

Reorder the terms:
ant(-20 + 3x) = cot(x + 18)
(-20 * ant + 3x * ant) = cot(x + 18)
(-20ant + 3antx) = cot(x + 18)

Reorder the terms:
-20ant + 3antx = cot(18 + x)
-20ant + 3antx = (18 * cot + x * cot)
-20ant + 3antx = (18cot + cotx)

Solving
-20ant + 3antx = 18cot + cotx

Solving for variable 'a'.

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

Reorder the terms:
-20ant + 3antx + -18cot + -1cotx = 18cot + -18cot + cotx + -1cotx

Combine like terms: 18cot + -18cot = 0
-20ant + 3antx + -18cot + -1cotx = 0 + cotx + -1cotx
-20ant + 3antx + -18cot + -1cotx = cotx + -1cotx

Combine like terms: cotx + -1cotx = 0
-20ant + 3antx + -18cot + -1cotx = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-20an + 3anx + -18co + -1cox) = 0


Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Add '-1t' to each side of the equation.
t + -1t = 0 + -1t
Remove the zero:
0 = -1t

Simplifying
0 = -1t

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-20an + 3anx + -18co + -1cox)' equal to zero and attempt to solve:

Simplifying
-20an + 3anx + -18co + -1cox = 0

Solving
-20an + 3anx + -18co + -1cox = 0

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

Add '18co' to each side of the equation.
-20an + 3anx + -18co + 18co + -1cox = 0 + 18co

Combine like terms: -18co + 18co = 0
-20an + 3anx + 0 + -1cox = 0 + 18co
-20an + 3anx + -1cox = 0 + 18co
Remove the zero:
-20an + 3anx + -1cox = 18co

Add 'cox' to each side of the equation.
-20an + 3anx + -1cox + cox = 18co + cox

Combine like terms: -1cox + cox = 0
-20an + 3anx + 0 = 18co + cox
-20an + 3anx = 18co + cox

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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