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Simplifying (14x5 + 7x3 + x) + -1(x + 20)(2nx2 + 1) = 14x5 + -15x3 + -440x2 + -20 Reorder the terms: (x + 7x3 + 14x5) + -1(x + 20)(2nx2 + 1) = 14x5 + -15x3 + -440x2 + -20 Remove parenthesis around (x + 7x3 + 14x5) x + 7x3 + 14x5 + -1(x + 20)(2nx2 + 1) = 14x5 + -15x3 + -440x2 + -20 Reorder the terms: x + 7x3 + 14x5 + -1(20 + x)(2nx2 + 1) = 14x5 + -15x3 + -440x2 + -20 Reorder the terms: x + 7x3 + 14x5 + -1(20 + x)(1 + 2nx2) = 14x5 + -15x3 + -440x2 + -20 Multiply (20 + x) * (1 + 2nx2) x + 7x3 + 14x5 + -1(20(1 + 2nx2) + x(1 + 2nx2)) = 14x5 + -15x3 + -440x2 + -20 x + 7x3 + 14x5 + -1((1 * 20 + 2nx2 * 20) + x(1 + 2nx2)) = 14x5 + -15x3 + -440x2 + -20 x + 7x3 + 14x5 + -1((20 + 40nx2) + x(1 + 2nx2)) = 14x5 + -15x3 + -440x2 + -20 x + 7x3 + 14x5 + -1(20 + 40nx2 + (1 * x + 2nx2 * x)) = 14x5 + -15x3 + -440x2 + -20 Reorder the terms: x + 7x3 + 14x5 + -1(20 + 40nx2 + (2nx3 + 1x)) = 14x5 + -15x3 + -440x2 + -20 x + 7x3 + 14x5 + -1(20 + 40nx2 + (2nx3 + 1x)) = 14x5 + -15x3 + -440x2 + -20 x + 7x3 + 14x5 + -1(20 + 40nx2 + 2nx3 + 1x) = 14x5 + -15x3 + -440x2 + -20 x + 7x3 + 14x5 + (20 * -1 + 40nx2 * -1 + 2nx3 * -1 + 1x * -1) = 14x5 + -15x3 + -440x2 + -20 x + 7x3 + 14x5 + (-20 + -40nx2 + -2nx3 + -1x) = 14x5 + -15x3 + -440x2 + -20 Reorder the terms: -20 + -40nx2 + -2nx3 + x + -1x + 7x3 + 14x5 = 14x5 + -15x3 + -440x2 + -20 Combine like terms: x + -1x = 0 -20 + -40nx2 + -2nx3 + 0 + 7x3 + 14x5 = 14x5 + -15x3 + -440x2 + -20 -20 + -40nx2 + -2nx3 + 7x3 + 14x5 = 14x5 + -15x3 + -440x2 + -20 Reorder the terms: -20 + -40nx2 + -2nx3 + 7x3 + 14x5 = -20 + -440x2 + -15x3 + 14x5 Add '20' to each side of the equation. -20 + -40nx2 + -2nx3 + 7x3 + 20 + 14x5 = -20 + -440x2 + -15x3 + 20 + 14x5 Reorder the terms: -20 + 20 + -40nx2 + -2nx3 + 7x3 + 14x5 = -20 + -440x2 + -15x3 + 20 + 14x5 Combine like terms: -20 + 20 = 0 0 + -40nx2 + -2nx3 + 7x3 + 14x5 = -20 + -440x2 + -15x3 + 20 + 14x5 -40nx2 + -2nx3 + 7x3 + 14x5 = -20 + -440x2 + -15x3 + 20 + 14x5 Reorder the terms: -40nx2 + -2nx3 + 7x3 + 14x5 = -20 + 20 + -440x2 + -15x3 + 14x5 Combine like terms: -20 + 20 = 0 -40nx2 + -2nx3 + 7x3 + 14x5 = 0 + -440x2 + -15x3 + 14x5 -40nx2 + -2nx3 + 7x3 + 14x5 = -440x2 + -15x3 + 14x5 Add '-14x5' to each side of the equation. -40nx2 + -2nx3 + 7x3 + 14x5 + -14x5 = -440x2 + -15x3 + 14x5 + -14x5 Combine like terms: 14x5 + -14x5 = 0 -40nx2 + -2nx3 + 7x3 + 0 = -440x2 + -15x3 + 14x5 + -14x5 -40nx2 + -2nx3 + 7x3 = -440x2 + -15x3 + 14x5 + -14x5 Combine like terms: 14x5 + -14x5 = 0 -40nx2 + -2nx3 + 7x3 = -440x2 + -15x3 + 0 -40nx2 + -2nx3 + 7x3 = -440x2 + -15x3 Solving -40nx2 + -2nx3 + 7x3 = -440x2 + -15x3 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-7x3' to each side of the equation. -40nx2 + -2nx3 + 7x3 + -7x3 = -440x2 + -15x3 + -7x3 Combine like terms: 7x3 + -7x3 = 0 -40nx2 + -2nx3 + 0 = -440x2 + -15x3 + -7x3 -40nx2 + -2nx3 = -440x2 + -15x3 + -7x3 Combine like terms: -15x3 + -7x3 = -22x3 -40nx2 + -2nx3 = -440x2 + -22x3 Reorder the terms: -40nx2 + -2nx3 + 440x2 + 22x3 = -440x2 + 440x2 + -22x3 + 22x3 Combine like terms: -440x2 + 440x2 = 0 -40nx2 + -2nx3 + 440x2 + 22x3 = 0 + -22x3 + 22x3 -40nx2 + -2nx3 + 440x2 + 22x3 = -22x3 + 22x3 Combine like terms: -22x3 + 22x3 = 0 -40nx2 + -2nx3 + 440x2 + 22x3 = 0 Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(-20n + -1nx + 220 + 11x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + -1x2 = 0 + -1x2 Remove the zero: 0 = -1x2 Simplifying 0 = -1x2 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 '(-20n + -1nx + 220 + 11x)' equal to zero and attempt to solve: Simplifying -20n + -1nx + 220 + 11x = 0 Reorder the terms: 220 + -20n + -1nx + 11x = 0 Solving 220 + -20n + -1nx + 11x = 0 Move all terms containing n to the left, all other terms to the right. Add '-220' to each side of the equation. 220 + -20n + -1nx + -220 + 11x = 0 + -220 Reorder the terms: 220 + -220 + -20n + -1nx + 11x = 0 + -220 Combine like terms: 220 + -220 = 0 0 + -20n + -1nx + 11x = 0 + -220 -20n + -1nx + 11x = 0 + -220 Combine like terms: 0 + -220 = -220 -20n + -1nx + 11x = -220 Add '-11x' to each side of the equation. -20n + -1nx + 11x + -11x = -220 + -11x Combine like terms: 11x + -11x = 0 -20n + -1nx + 0 = -220 + -11x -20n + -1nx = -220 + -11x 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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