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Simplifying log(-35 + 3x2) = log(4x2 + -12x) (-35 * glo + 3x2 * glo) = log(4x2 + -12x) (-35glo + 3glox2) = log(4x2 + -12x) Reorder the terms: -35glo + 3glox2 = glo(-12x + 4x2) -35glo + 3glox2 = (-12x * glo + 4x2 * glo) -35glo + 3glox2 = (-12glox + 4glox2) Solving -35glo + 3glox2 = -12glox + 4glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '12glox' to each side of the equation. -35glo + 12glox + 3glox2 = -12glox + 12glox + 4glox2 Combine like terms: -12glox + 12glox = 0 -35glo + 12glox + 3glox2 = 0 + 4glox2 -35glo + 12glox + 3glox2 = 4glox2 Add '-4glox2' to each side of the equation. -35glo + 12glox + 3glox2 + -4glox2 = 4glox2 + -4glox2 Combine like terms: 3glox2 + -4glox2 = -1glox2 -35glo + 12glox + -1glox2 = 4glox2 + -4glox2 Combine like terms: 4glox2 + -4glox2 = 0 -35glo + 12glox + -1glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-35 + 12x + -1x2) = 0 Factor a trinomial. glo((-7 + x)(5 + -1x)) = 0Subproblem 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 '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Add '-1x' to each side of the equation. x + -1x = 7 + -1x Combine like terms: x + -1x = 0 0 = 7 + -1x Simplifying 0 = 7 + -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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + x 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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