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Simplifying tlog(6t + 1) + -3t2log(6t + 1) = 0 Reorder the terms: glot(1 + 6t) + -3t2log(6t + 1) = 0 (1 * glot + 6t * glot) + -3t2log(6t + 1) = 0 (1glot + 6glot2) + -3t2log(6t + 1) = 0 Reorder the terms: 1glot + 6glot2 + -3glot2(1 + 6t) = 0 1glot + 6glot2 + (1 * -3glot2 + 6t * -3glot2) = 0 1glot + 6glot2 + (-3glot2 + -18glot3) = 0 Combine like terms: 6glot2 + -3glot2 = 3glot2 1glot + 3glot2 + -18glot3 = 0 Solving 1glot + 3glot2 + -18glot3 = 0 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'glot'. glot(1 + 3t + -18t2) = 0 Factor a trinomial. glot((1 + -3t)(1 + 6t)) = 0Subproblem 1
Set the factor 'glot' equal to zero and attempt to solve: Simplifying glot = 0 Solving glot = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glot = 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 + -3t)' equal to zero and attempt to solve: Simplifying 1 + -3t = 0 Solving 1 + -3t = 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 + -3t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3t = 0 + -1 -3t = 0 + -1 Combine like terms: 0 + -1 = -1 -3t = -1 Add '3t' to each side of the equation. -3t + 3t = -1 + 3t Combine like terms: -3t + 3t = 0 0 = -1 + 3t Simplifying 0 = -1 + 3t 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 + 6t)' equal to zero and attempt to solve: Simplifying 1 + 6t = 0 Solving 1 + 6t = 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 + 6t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6t = 0 + -1 6t = 0 + -1 Combine like terms: 0 + -1 = -1 6t = -1 Add '-6t' to each side of the equation. 6t + -6t = -1 + -6t Combine like terms: 6t + -6t = 0 0 = -1 + -6t Simplifying 0 = -1 + -6t 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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