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Simplifying -3n(4x + 3) + 4(6x + 1) = 43 Reorder the terms: -3n(3 + 4x) + 4(6x + 1) = 43 (3 * -3n + 4x * -3n) + 4(6x + 1) = 43 (-9n + -12nx) + 4(6x + 1) = 43 Reorder the terms: -9n + -12nx + 4(1 + 6x) = 43 -9n + -12nx + (1 * 4 + 6x * 4) = 43 -9n + -12nx + (4 + 24x) = 43 Reorder the terms: 4 + -9n + -12nx + 24x = 43 Solving 4 + -9n + -12nx + 24x = 43 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -9n + -12nx + -4 + 24x = 43 + -4 Reorder the terms: 4 + -4 + -9n + -12nx + 24x = 43 + -4 Combine like terms: 4 + -4 = 0 0 + -9n + -12nx + 24x = 43 + -4 -9n + -12nx + 24x = 43 + -4 Combine like terms: 43 + -4 = 39 -9n + -12nx + 24x = 39 Add '-24x' to each side of the equation. -9n + -12nx + 24x + -24x = 39 + -24x Combine like terms: 24x + -24x = 0 -9n + -12nx + 0 = 39 + -24x -9n + -12nx = 39 + -24x Reorder the terms: -39 + -9n + -12nx + 24x = 39 + -24x + -39 + 24x Reorder the terms: -39 + -9n + -12nx + 24x = 39 + -39 + -24x + 24x Combine like terms: 39 + -39 = 0 -39 + -9n + -12nx + 24x = 0 + -24x + 24x -39 + -9n + -12nx + 24x = -24x + 24x Combine like terms: -24x + 24x = 0 -39 + -9n + -12nx + 24x = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-13 + -3n + -4nx + 8x) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-13 + -3n + -4nx + 8x)' equal to zero and attempt to solve: Simplifying -13 + -3n + -4nx + 8x = 0 Solving -13 + -3n + -4nx + 8x = 0 Move all terms containing n to the left, all other terms to the right. Add '13' to each side of the equation. -13 + -3n + -4nx + 13 + 8x = 0 + 13 Reorder the terms: -13 + 13 + -3n + -4nx + 8x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -3n + -4nx + 8x = 0 + 13 -3n + -4nx + 8x = 0 + 13 Combine like terms: 0 + 13 = 13 -3n + -4nx + 8x = 13 Add '-8x' to each side of the equation. -3n + -4nx + 8x + -8x = 13 + -8x Combine like terms: 8x + -8x = 0 -3n + -4nx + 0 = 13 + -8x -3n + -4nx = 13 + -8x 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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