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Simplifying (6n + 8) * x(6n + 1) = 0 Reorder the terms: (8 + 6n) * x(6n + 1) = 0 Reorder the terms: (8 + 6n) * x(1 + 6n) = 0 Reorder the terms for easier multiplication: x(8 + 6n)(1 + 6n) = 0 Multiply (8 + 6n) * (1 + 6n) x(8(1 + 6n) + 6n * (1 + 6n)) = 0 x((1 * 8 + 6n * 8) + 6n * (1 + 6n)) = 0 x((8 + 48n) + 6n * (1 + 6n)) = 0 x(8 + 48n + (1 * 6n + 6n * 6n)) = 0 x(8 + 48n + (6n + 36n2)) = 0 Combine like terms: 48n + 6n = 54n x(8 + 54n + 36n2) = 0 (8 * x + 54n * x + 36n2 * x) = 0 Reorder the terms: (54nx + 36n2x + 8x) = 0 (54nx + 36n2x + 8x) = 0 Solving 54nx + 36n2x + 8x = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(27n + 18n2 + 4) = 0 Factor a trinomial. 2x((6n + 1)(3n + 4)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing n to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x 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 '(6n + 1)' equal to zero and attempt to solve: Simplifying 6n + 1 = 0 Reorder the terms: 1 + 6n = 0 Solving 1 + 6n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 6n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6n = 0 + -1 6n = 0 + -1 Combine like terms: 0 + -1 = -1 6n = -1 Divide each side by '6'. n = -0.1666666667 Simplifying n = -0.1666666667Subproblem 3
Set the factor '(3n + 4)' equal to zero and attempt to solve: Simplifying 3n + 4 = 0 Reorder the terms: 4 + 3n = 0 Solving 4 + 3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3n = 0 + -4 3n = 0 + -4 Combine like terms: 0 + -4 = -4 3n = -4 Divide each side by '3'. n = -1.333333333 Simplifying n = -1.333333333Solution
n = {-0.1666666667, -1.333333333}
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