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Simplifying lg(x2 + -1x + -6) + -1lg(x + -3) = 0 Reorder the terms: gl(-6 + -1x + x2) + -1lg(x + -3) = 0 (-6 * gl + -1x * gl + x2 * gl) + -1lg(x + -3) = 0 (-6gl + -1glx + glx2) + -1lg(x + -3) = 0 Reorder the terms: -6gl + -1glx + glx2 + -1gl(-3 + x) = 0 -6gl + -1glx + glx2 + (-3 * -1gl + x * -1gl) = 0 -6gl + -1glx + glx2 + (3gl + -1glx) = 0 Reorder the terms: -6gl + 3gl + -1glx + -1glx + glx2 = 0 Combine like terms: -6gl + 3gl = -3gl -3gl + -1glx + -1glx + glx2 = 0 Combine like terms: -1glx + -1glx = -2glx -3gl + -2glx + glx2 = 0 Solving -3gl + -2glx + glx2 = 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), 'gl'. gl(-3 + -2x + x2) = 0 Factor a trinomial. gl((-1 + -1x)(3 + -1x)) = 0Subproblem 1
Set the factor 'gl' equal to zero and attempt to solve: Simplifying gl = 0 Solving gl = 0 Move all terms containing g to the left, all other terms to the right. Simplifying gl = 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 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Add 'x' to each side of the equation. -1x + x = 1 + x Combine like terms: -1x + x = 0 0 = 1 + x Simplifying 0 = 1 + x 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + 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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