tg(x)+stg(2x)=ctg(x)-4ctg(4x)

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Solution for tg(x)+stg(2x)=ctg(x)-4ctg(4x) equation:


Simplifying
tg(x) + stg(2x) = ctg(x) + -4ctg(4x)

Multiply gt * x
gtx + stg(2x) = ctg(x) + -4ctg(4x)

Remove parenthesis around (2x)
gtx + gst * 2x = ctg(x) + -4ctg(4x)

Reorder the terms for easier multiplication:
gtx + 2gst * x = ctg(x) + -4ctg(4x)

Multiply gst * x
gtx + 2gstx = ctg(x) + -4ctg(4x)

Reorder the terms:
2gstx + gtx = ctg(x) + -4ctg(4x)

Multiply cgt * x
2gstx + gtx = cgtx + -4ctg(4x)

Remove parenthesis around (4x)
2gstx + gtx = cgtx + -4cgt * 4x

Reorder the terms for easier multiplication:
2gstx + gtx = cgtx + -4 * 4cgt * x

Multiply -4 * 4
2gstx + gtx = cgtx + -16cgt * x

Multiply cgt * x
2gstx + gtx = cgtx + -16cgtx

Combine like terms: cgtx + -16cgtx = -15cgtx
2gstx + gtx = -15cgtx

Solving
2gstx + gtx = -15cgtx

Solving for variable 'g'.

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

Add '15cgtx' to each side of the equation.
2gstx + 15cgtx + gtx = -15cgtx + 15cgtx

Reorder the terms:
15cgtx + 2gstx + gtx = -15cgtx + 15cgtx

Combine like terms: -15cgtx + 15cgtx = 0
15cgtx + 2gstx + gtx = 0

Factor out the Greatest Common Factor (GCF), 'gtx'.
gtx(15c + 2s + 1) = 0

Subproblem 1

Set the factor 'gtx' equal to zero and attempt to solve: Simplifying gtx = 0 Solving gtx = 0 Move all terms containing g to the left, all other terms to the right. Simplifying gtx = 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 '(15c + 2s + 1)' equal to zero and attempt to solve: Simplifying 15c + 2s + 1 = 0 Reorder the terms: 1 + 15c + 2s = 0 Solving 1 + 15c + 2s = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 15c + -1 + 2s = 0 + -1 Reorder the terms: 1 + -1 + 15c + 2s = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 15c + 2s = 0 + -1 15c + 2s = 0 + -1 Combine like terms: 0 + -1 = -1 15c + 2s = -1 Add '-15c' to each side of the equation. 15c + -15c + 2s = -1 + -15c Combine like terms: 15c + -15c = 0 0 + 2s = -1 + -15c 2s = -1 + -15c Add '-2s' to each side of the equation. 2s + -2s = -1 + -15c + -2s Combine like terms: 2s + -2s = 0 0 = -1 + -15c + -2s Simplifying 0 = -1 + -15c + -2s 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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