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Simplifying 0 = Log(x2 + -6x + 8) Reorder the terms: 0 = goL(8 + -6x + x2) 0 = (8 * goL + -6x * goL + x2 * goL) 0 = (8goL + -6goxL + gox2L) Solving 0 = 8goL + -6goxL + gox2L Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-8goL' to each side of the equation. 0 + -8goL = 8goL + -6goxL + -8goL + gox2L Remove the zero: -8goL = 8goL + -6goxL + -8goL + gox2L Reorder the terms: -8goL = 8goL + -8goL + -6goxL + gox2L Combine like terms: 8goL + -8goL = 0 -8goL = 0 + -6goxL + gox2L -8goL = -6goxL + gox2L Add '6goxL' to each side of the equation. -8goL + 6goxL = -6goxL + 6goxL + gox2L Combine like terms: -6goxL + 6goxL = 0 -8goL + 6goxL = 0 + gox2L -8goL + 6goxL = gox2L Add '-1gox2L' to each side of the equation. -8goL + 6goxL + -1gox2L = gox2L + -1gox2L Combine like terms: gox2L + -1gox2L = 0 -8goL + 6goxL + -1gox2L = 0 Factor out the Greatest Common Factor (GCF), 'goL'. goL(-8 + 6x + -1x2) = 0 Factor a trinomial. goL((-4 + x)(2 + -1x)) = 0Subproblem 1
Set the factor 'goL' equal to zero and attempt to solve: Simplifying goL = 0 Solving goL = 0 Move all terms containing g to the left, all other terms to the right. Simplifying goL = 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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + 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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