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Simplifying tg(x) + 2tg(2x) = ctg(x) + -4ctg(4x) Multiply gt * x gtx + 2tg(2x) = ctg(x) + -4ctg(4x) Remove parenthesis around (2x) gtx + 2gt * 2x = ctg(x) + -4ctg(4x) Reorder the terms for easier multiplication: gtx + 2 * 2gt * x = ctg(x) + -4ctg(4x) Multiply 2 * 2 gtx + 4gt * x = ctg(x) + -4ctg(4x) Multiply gt * x gtx + 4gtx = ctg(x) + -4ctg(4x) Combine like terms: gtx + 4gtx = 5gtx 5gtx = ctg(x) + -4ctg(4x) Multiply cgt * x 5gtx = cgtx + -4ctg(4x) Remove parenthesis around (4x) 5gtx = cgtx + -4cgt * 4x Reorder the terms for easier multiplication: 5gtx = cgtx + -4 * 4cgt * x Multiply -4 * 4 5gtx = cgtx + -16cgt * x Multiply cgt * x 5gtx = cgtx + -16cgtx Combine like terms: cgtx + -16cgtx = -15cgtx 5gtx = -15cgtx Solving 5gtx = -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. 15cgtx + 5gtx = -15cgtx + 15cgtx Combine like terms: -15cgtx + 15cgtx = 0 15cgtx + 5gtx = 0 Factor out the Greatest Common Factor (GCF), '5gtx'. 5gtx(3c + 1) = 0 Ignore the factor 5.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 '(3c + 1)' equal to zero and attempt to solve: Simplifying 3c + 1 = 0 Reorder the terms: 1 + 3c = 0 Solving 1 + 3c = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3c = 0 + -1 3c = 0 + -1 Combine like terms: 0 + -1 = -1 3c = -1 Add '-3c' to each side of the equation. 3c + -3c = -1 + -3c Combine like terms: 3c + -3c = 0 0 = -1 + -3c Simplifying 0 = -1 + -3c 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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