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Simplifying 12 = 6ln(28t + 1) * find(t) Reorder the terms: 12 = 6ln(1 + 28t) * find(t) Reorder the terms for easier multiplication: 12 = 6ln * dfin * t(1 + 28t) Multiply ln * dfin 12 = 6dfiln2 * t(1 + 28t) Multiply dfiln2 * t 12 = 6dfiln2t(1 + 28t) 12 = (1 * 6dfiln2t + 28t * 6dfiln2t) 12 = (6dfiln2t + 168dfiln2t2) Solving 12 = 6dfiln2t + 168dfiln2t2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-6dfiln2t' to each side of the equation. 12 + -6dfiln2t = 6dfiln2t + -6dfiln2t + 168dfiln2t2 Combine like terms: 6dfiln2t + -6dfiln2t = 0 12 + -6dfiln2t = 0 + 168dfiln2t2 12 + -6dfiln2t = 168dfiln2t2 Add '-168dfiln2t2' to each side of the equation. 12 + -6dfiln2t + -168dfiln2t2 = 168dfiln2t2 + -168dfiln2t2 Combine like terms: 168dfiln2t2 + -168dfiln2t2 = 0 12 + -6dfiln2t + -168dfiln2t2 = 0 Add '-12' to each side of the equation. 12 + -6dfiln2t + -12 + -168dfiln2t2 = 0 + -12 Reorder the terms: 12 + -12 + -6dfiln2t + -168dfiln2t2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -6dfiln2t + -168dfiln2t2 = 0 + -12 -6dfiln2t + -168dfiln2t2 = 0 + -12 Combine like terms: 0 + -12 = -12 -6dfiln2t + -168dfiln2t2 = -12 Reorder the terms: 12 + -6dfiln2t + -168dfiln2t2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + -6dfiln2t + -168dfiln2t2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(2 + -1dfiln2t + -28dfiln2t2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(2 + -1dfiln2t + -28dfiln2t2)' equal to zero and attempt to solve: Simplifying 2 + -1dfiln2t + -28dfiln2t2 = 0 Solving 2 + -1dfiln2t + -28dfiln2t2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -1dfiln2t + -2 + -28dfiln2t2 = 0 + -2 Reorder the terms: 2 + -2 + -1dfiln2t + -28dfiln2t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1dfiln2t + -28dfiln2t2 = 0 + -2 -1dfiln2t + -28dfiln2t2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1dfiln2t + -28dfiln2t2 = -2 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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