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Simplifying In(3x + -3) = in(x + -6) Reorder the terms: nI(-3 + 3x) = in(x + -6) (-3 * nI + 3x * nI) = in(x + -6) (-3nI + 3nxI) = in(x + -6) Reorder the terms: -3nI + 3nxI = in(-6 + x) -3nI + 3nxI = (-6 * in + x * in) -3nI + 3nxI = (-6in + inx) Solving -3nI + 3nxI = -6in + inx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6in' to each side of the equation. -3nI + 6in + 3nxI = -6in + 6in + inx Reorder the terms: 6in + -3nI + 3nxI = -6in + 6in + inx Combine like terms: -6in + 6in = 0 6in + -3nI + 3nxI = 0 + inx 6in + -3nI + 3nxI = inx Add '-1inx' to each side of the equation. 6in + -3nI + -1inx + 3nxI = inx + -1inx Reorder the terms: 6in + -1inx + -3nI + 3nxI = inx + -1inx Combine like terms: inx + -1inx = 0 6in + -1inx + -3nI + 3nxI = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(6i + -1ix + -3I + 3xI) = 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 '(6i + -1ix + -3I + 3xI)' equal to zero and attempt to solve: Simplifying 6i + -1ix + -3I + 3xI = 0 Reorder the terms: -3I + 6i + -1ix + 3xI = 0 Solving -3I + 6i + -1ix + 3xI = 0 Move all terms containing n to the left, all other terms to the right. Add '3I' to each side of the equation. -3I + 6i + -1ix + 3I + 3xI = 0 + 3I Reorder the terms: -3I + 3I + 6i + -1ix + 3xI = 0 + 3I Combine like terms: -3I + 3I = 0 0 + 6i + -1ix + 3xI = 0 + 3I 6i + -1ix + 3xI = 0 + 3I Remove the zero: 6i + -1ix + 3xI = 3I Add '-6i' to each side of the equation. 6i + -1ix + -6i + 3xI = 3I + -6i Reorder the terms: 6i + -6i + -1ix + 3xI = 3I + -6i Combine like terms: 6i + -6i = 0 0 + -1ix + 3xI = 3I + -6i -1ix + 3xI = 3I + -6i Add 'ix' to each side of the equation. -1ix + ix + 3xI = 3I + -6i + ix Combine like terms: -1ix + ix = 0 0 + 3xI = 3I + -6i + ix 3xI = 3I + -6i + ix Add '-3xI' to each side of the equation. 3xI + -3xI = 3I + -6i + ix + -3xI Combine like terms: 3xI + -3xI = 0 0 = 3I + -6i + ix + -3xI Simplifying 0 = 3I + -6i + ix + -3xI 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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