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Simplifying ln(4x + -1) * ln(5x + -1) = 0 Reorder the terms: ln(-1 + 4x) * ln(5x + -1) = 0 Reorder the terms: ln(-1 + 4x) * ln(-1 + 5x) = 0 Reorder the terms for easier multiplication: ln * ln(-1 + 4x)(-1 + 5x) = 0 Multiply ln * ln l2n2(-1 + 4x)(-1 + 5x) = 0 Multiply (-1 + 4x) * (-1 + 5x) l2n2(-1(-1 + 5x) + 4x * (-1 + 5x)) = 0 l2n2((-1 * -1 + 5x * -1) + 4x * (-1 + 5x)) = 0 l2n2((1 + -5x) + 4x * (-1 + 5x)) = 0 l2n2(1 + -5x + (-1 * 4x + 5x * 4x)) = 0 l2n2(1 + -5x + (-4x + 20x2)) = 0 Combine like terms: -5x + -4x = -9x l2n2(1 + -9x + 20x2) = 0 (1 * l2n2 + -9x * l2n2 + 20x2 * l2n2) = 0 (1l2n2 + -9l2n2x + 20l2n2x2) = 0 Solving 1l2n2 + -9l2n2x + 20l2n2x2 = 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), 'l2n2'. l2n2(1 + -9x + 20x2) = 0 Factor a trinomial. l2n2((1 + -5x)(1 + -4x)) = 0Subproblem 1
Set the factor 'l2n2' equal to zero and attempt to solve: Simplifying l2n2 = 0 Solving l2n2 = 0 Move all terms containing l to the left, all other terms to the right. Simplifying l2n2 = 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 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 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 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Add '5x' to each side of the equation. -5x + 5x = -1 + 5x Combine like terms: -5x + 5x = 0 0 = -1 + 5x Simplifying 0 = -1 + 5x 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 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Add '4x' to each side of the equation. -4x + 4x = -1 + 4x Combine like terms: -4x + 4x = 0 0 = -1 + 4x Simplifying 0 = -1 + 4x 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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