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Simplifying -6n + -20 = -2n + 4x(1 + -3n) Reorder the terms: -20 + -6n = -2n + 4x(1 + -3n) -20 + -6n = -2n + (1 * 4x + -3n * 4x) Reorder the terms: -20 + -6n = -2n + (-12nx + 4x) -20 + -6n = -2n + (-12nx + 4x) Solving -20 + -6n = -2n + -12nx + 4x Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2n' to each side of the equation. -20 + -6n + 2n = -2n + -12nx + 2n + 4x Combine like terms: -6n + 2n = -4n -20 + -4n = -2n + -12nx + 2n + 4x Reorder the terms: -20 + -4n = -2n + 2n + -12nx + 4x Combine like terms: -2n + 2n = 0 -20 + -4n = 0 + -12nx + 4x -20 + -4n = -12nx + 4x Add '12nx' to each side of the equation. -20 + -4n + 12nx = -12nx + 12nx + 4x Combine like terms: -12nx + 12nx = 0 -20 + -4n + 12nx = 0 + 4x -20 + -4n + 12nx = 4x Add '20' to each side of the equation. -20 + -4n + 20 + 12nx = 20 + 4x Reorder the terms: -20 + 20 + -4n + 12nx = 20 + 4x Combine like terms: -20 + 20 = 0 0 + -4n + 12nx = 20 + 4x -4n + 12nx = 20 + 4x Reorder the terms: -20 + -4n + 12nx + -4x = 20 + 4x + -20 + -4x Reorder the terms: -20 + -4n + 12nx + -4x = 20 + -20 + 4x + -4x Combine like terms: 20 + -20 = 0 -20 + -4n + 12nx + -4x = 0 + 4x + -4x -20 + -4n + 12nx + -4x = 4x + -4x Combine like terms: 4x + -4x = 0 -20 + -4n + 12nx + -4x = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -1n + 3nx + -1x) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -1n + 3nx + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1n + 3nx + -1x = 0 Solving -5 + -1n + 3nx + -1x = 0 Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + -1n + 3nx + 5 + -1x = 0 + 5 Reorder the terms: -5 + 5 + -1n + 3nx + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1n + 3nx + -1x = 0 + 5 -1n + 3nx + -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1n + 3nx + -1x = 5 Add 'x' to each side of the equation. -1n + 3nx + -1x + x = 5 + x Combine like terms: -1x + x = 0 -1n + 3nx + 0 = 5 + x -1n + 3nx = 5 + x 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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