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Simplifying 27tan5x = 3tan3x Solving 27an5tx = 3an3tx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3an3tx' to each side of the equation. -3an3tx + 27an5tx = 3an3tx + -3an3tx Combine like terms: 3an3tx + -3an3tx = 0 -3an3tx + 27an5tx = 0 Factor out the Greatest Common Factor (GCF), '3an3tx'. 3an3tx(-1 + 9n2) = 0 Factor a difference between two squares. 3an3tx((1 + 3n)(-1 + 3n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'an3tx' equal to zero and attempt to solve: Simplifying an3tx = 0 Solving an3tx = 0 Move all terms containing a to the left, all other terms to the right. Simplifying an3tx = 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 '(1 + 3n)' equal to zero and attempt to solve: Simplifying 1 + 3n = 0 Solving 1 + 3n = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3n = 0 + -1 3n = 0 + -1 Combine like terms: 0 + -1 = -1 3n = -1 Add '-3n' to each side of the equation. 3n + -3n = -1 + -3n Combine like terms: 3n + -3n = 0 0 = -1 + -3n Simplifying 0 = -1 + -3n The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-1 + 3n)' equal to zero and attempt to solve: Simplifying -1 + 3n = 0 Solving -1 + 3n = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 3n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3n = 0 + 1 3n = 0 + 1 Combine like terms: 0 + 1 = 1 3n = 1 Add '-3n' to each side of the equation. 3n + -3n = 1 + -3n Combine like terms: 3n + -3n = 0 0 = 1 + -3n Simplifying 0 = 1 + -3n 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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