tan(2*x)*tan(x)=tan(5*x)

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Solution for tan(2*x)*tan(x)=tan(5*x) equation: 


Simplifying
tan(2x) * tan(x) = tan(5x)

Remove parenthesis around (2x)
ant * 2x * tan(x) = tan(5x)

Reorder the terms for easier multiplication:
2ant * x * ant * x = tan(5x)

Multiply ant * x
2antx * ant * x = tan(5x)

Multiply antx * ant
2a2n2t2x * x = tan(5x)

Multiply a2n2t2x * x
2a2n2t2x2 = tan(5x)

Remove parenthesis around (5x)
2a2n2t2x2 = ant * 5x

Reorder the terms for easier multiplication:
2a2n2t2x2 = 5ant * x

Multiply ant * x
2a2n2t2x2 = 5antx

Solving
2a2n2t2x2 = 5antx

Solving for variable 'a'.

Reorder the terms:
-5antx + 2a2n2t2x2 = 5antx + -5antx

Combine like terms: 5antx + -5antx = 0
-5antx + 2a2n2t2x2 = 0

Factor out the Greatest Common Factor (GCF), 'antx'.
antx(-5 + 2antx) = 0


Subproblem 1
Set the factor 'antx' equal to zero and attempt to solve:

Simplifying
antx = 0

Solving
antx = 0

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

Simplifying
antx = 0

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 '(-5 + 2antx)' equal to zero and attempt to solve:

Simplifying
-5 + 2antx = 0

Solving
-5 + 2antx = 0

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

Add '5' to each side of the equation.
-5 + 5 + 2antx = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2antx = 0 + 5
2antx = 0 + 5

Combine like terms: 0 + 5 = 5
2antx = 5

Divide each side by '2ntx'.
a = 2.5n-1t-1x-1

Simplifying
a = 2.5n-1t-1x-1
Solution
a = {2.5n-1t-1x-1}

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