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Simplifying In(5x + -1) = in(3x + 2) Reorder the terms: nI(-1 + 5x) = in(3x + 2) (-1 * nI + 5x * nI) = in(3x + 2) (-1nI + 5nxI) = in(3x + 2) Reorder the terms: -1nI + 5nxI = in(2 + 3x) -1nI + 5nxI = (2 * in + 3x * in) -1nI + 5nxI = (2in + 3inx) Solving -1nI + 5nxI = 2in + 3inx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2in' to each side of the equation. -1nI + -2in + 5nxI = 2in + -2in + 3inx Reorder the terms: -2in + -1nI + 5nxI = 2in + -2in + 3inx Combine like terms: 2in + -2in = 0 -2in + -1nI + 5nxI = 0 + 3inx -2in + -1nI + 5nxI = 3inx Add '-3inx' to each side of the equation. -2in + -1nI + -3inx + 5nxI = 3inx + -3inx Reorder the terms: -2in + -3inx + -1nI + 5nxI = 3inx + -3inx Combine like terms: 3inx + -3inx = 0 -2in + -3inx + -1nI + 5nxI = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-2i + -3ix + -1I + 5xI) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(-2i + -3ix + -1I + 5xI)' equal to zero and attempt to solve: Simplifying -2i + -3ix + -1I + 5xI = 0 Reorder the terms: -1I + -2i + -3ix + 5xI = 0 Solving -1I + -2i + -3ix + 5xI = 0 Move all terms containing n to the left, all other terms to the right. Add 'I' to each side of the equation. -1I + -2i + -3ix + I + 5xI = 0 + I Reorder the terms: -1I + I + -2i + -3ix + 5xI = 0 + I Combine like terms: -1I + I = 0 0 + -2i + -3ix + 5xI = 0 + I -2i + -3ix + 5xI = 0 + I Remove the zero: -2i + -3ix + 5xI = I Add '2i' to each side of the equation. -2i + -3ix + 2i + 5xI = I + 2i Reorder the terms: -2i + 2i + -3ix + 5xI = I + 2i Combine like terms: -2i + 2i = 0 0 + -3ix + 5xI = I + 2i -3ix + 5xI = I + 2i Add '3ix' to each side of the equation. -3ix + 3ix + 5xI = I + 2i + 3ix Combine like terms: -3ix + 3ix = 0 0 + 5xI = I + 2i + 3ix 5xI = I + 2i + 3ix Add '-5xI' to each side of the equation. 5xI + -5xI = I + 2i + 3ix + -5xI Combine like terms: 5xI + -5xI = 0 0 = I + 2i + 3ix + -5xI Simplifying 0 = I + 2i + 3ix + -5xI The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
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