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Simplifying 9x2 * lnx + -6x * lnx = 8lnx Multiply x2 * lnx 9lnx3 + -6x * lnx = 8lnx Multiply x * lnx 9lnx3 + -6lnx2 = 8lnx Reorder the terms: -6lnx2 + 9lnx3 = 8lnx Solving -6lnx2 + 9lnx3 = 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8lnx' to each side of the equation. -6lnx2 + -8lnx + 9lnx3 = 8lnx + -8lnx Reorder the terms: -8lnx + -6lnx2 + 9lnx3 = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 -8lnx + -6lnx2 + 9lnx3 = 0 Factor out the Greatest Common Factor (GCF), 'lnx'. lnx(-8 + -6x + 9x2) = 0 Factor a trinomial. lnx((-2 + -3x)(4 + -3x)) = 0Subproblem 1
Set the factor 'lnx' equal to zero and attempt to solve: Simplifying lnx = 0 Solving lnx = 0 Move all terms containing l to the left, all other terms to the right. Simplifying lnx = 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 '(-2 + -3x)' equal to zero and attempt to solve: Simplifying -2 + -3x = 0 Solving -2 + -3x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3x = 0 + 2 -3x = 0 + 2 Combine like terms: 0 + 2 = 2 -3x = 2 Add '3x' to each side of the equation. -3x + 3x = 2 + 3x Combine like terms: -3x + 3x = 0 0 = 2 + 3x Simplifying 0 = 2 + 3x 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 '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Add '3x' to each side of the equation. -3x + 3x = -4 + 3x Combine like terms: -3x + 3x = 0 0 = -4 + 3x Simplifying 0 = -4 + 3x 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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