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Simplifying ln(x(x + 1)(x + 2)) = 0 Reorder the terms: ln(x(1 + x)(x + 2)) = 0 Reorder the terms: ln(x(1 + x)(2 + x)) = 0 Multiply (1 + x) * (2 + x) ln(x(1(2 + x) + x(2 + x))) = 0 ln(x((2 * 1 + x * 1) + x(2 + x))) = 0 ln(x((2 + 1x) + x(2 + x))) = 0 ln(x(2 + 1x + (2 * x + x * x))) = 0 ln(x(2 + 1x + (2x + x2))) = 0 Combine like terms: 1x + 2x = 3x ln(x(2 + 3x + x2)) = 0 ln((2 * x + 3x * x + x2 * x)) = 0 ln((2x + 3x2 + x3)) = 0 (2x * ln + 3x2 * ln + x3 * ln) = 0 (2lnx + 3lnx2 + lnx3) = 0 Solving 2lnx + 3lnx2 + lnx3 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'lnx'. lnx(2 + 3x + x2) = 0 Factor a trinomial. lnx((2 + x)(1 + x)) = 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 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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