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Simplifying log[12](x2 + 35) = log[12](-12x + -1) Reorder the terms: glo * 12(35 + x2) = log[12](-12x + -1) Reorder the terms for easier multiplication: 12glo(35 + x2) = log[12](-12x + -1) (35 * 12glo + x2 * 12glo) = log[12](-12x + -1) (420glo + 12glox2) = log[12](-12x + -1) Reorder the terms: 420glo + 12glox2 = glo * 12(-1 + -12x) Reorder the terms for easier multiplication: 420glo + 12glox2 = 12glo(-1 + -12x) 420glo + 12glox2 = (-1 * 12glo + -12x * 12glo) 420glo + 12glox2 = (-12glo + -144glox) Solving 420glo + 12glox2 = -12glo + -144glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '12glo' to each side of the equation. 420glo + 12glo + 12glox2 = -12glo + 12glo + -144glox Combine like terms: 420glo + 12glo = 432glo 432glo + 12glox2 = -12glo + 12glo + -144glox Combine like terms: -12glo + 12glo = 0 432glo + 12glox2 = 0 + -144glox 432glo + 12glox2 = -144glox Add '144glox' to each side of the equation. 432glo + 144glox + 12glox2 = -144glox + 144glox Combine like terms: -144glox + 144glox = 0 432glo + 144glox + 12glox2 = 0 Factor out the Greatest Common Factor (GCF), '12glo'. 12glo(36 + 12x + x2) = 0 Factor a trinomial. 12glo((6 + x)(6 + x)) = 0 Ignore the factor 12.Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -1x 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -1x 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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