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Simplifying lg(x + -1) = lg(x2 + -1x + -16) Reorder the terms: gl(-1 + x) = lg(x2 + -1x + -16) (-1 * gl + x * gl) = lg(x2 + -1x + -16) (-1gl + glx) = lg(x2 + -1x + -16) Reorder the terms: -1gl + glx = gl(-16 + -1x + x2) -1gl + glx = (-16 * gl + -1x * gl + x2 * gl) -1gl + glx = (-16gl + -1glx + glx2) Solving -1gl + glx = -16gl + -1glx + glx2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '16gl' to each side of the equation. -1gl + 16gl + glx = -16gl + -1glx + 16gl + glx2 Combine like terms: -1gl + 16gl = 15gl 15gl + glx = -16gl + -1glx + 16gl + glx2 Reorder the terms: 15gl + glx = -16gl + 16gl + -1glx + glx2 Combine like terms: -16gl + 16gl = 0 15gl + glx = 0 + -1glx + glx2 15gl + glx = -1glx + glx2 Add 'glx' to each side of the equation. 15gl + glx + glx = -1glx + glx + glx2 Combine like terms: glx + glx = 2glx 15gl + 2glx = -1glx + glx + glx2 Combine like terms: -1glx + glx = 0 15gl + 2glx = 0 + glx2 15gl + 2glx = glx2 Add '-1glx2' to each side of the equation. 15gl + 2glx + -1glx2 = glx2 + -1glx2 Combine like terms: glx2 + -1glx2 = 0 15gl + 2glx + -1glx2 = 0 Factor out the Greatest Common Factor (GCF), 'gl'. gl(15 + 2x + -1x2) = 0 Factor a trinomial. gl((5 + -1x)(3 + x)) = 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 '(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.Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -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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