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Simplifying (mx3 + 3)(2x2 + 5x + 2) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15x + 6 Reorder the terms: (3 + mx3)(2x2 + 5x + 2) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15x + 6 Reorder the terms: (3 + mx3)(2 + 5x + 2x2) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15x + 6 Multiply (3 + mx3) * (2 + 5x + 2x2) (3(2 + 5x + 2x2) + mx3(2 + 5x + 2x2)) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15x + 6 ((2 * 3 + 5x * 3 + 2x2 * 3) + mx3(2 + 5x + 2x2)) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15x + 6 ((6 + 15x + 6x2) + mx3(2 + 5x + 2x2)) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15x + 6 (6 + 15x + 6x2 + (2 * mx3 + 5x * mx3 + 2x2 * mx3)) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15x + 6 (6 + 15x + 6x2 + (2mx3 + 5mx4 + 2mx5)) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15x + 6 Reorder the terms: (6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15x + 6 (6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15x + 6 Reorder the terms: 6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -1(20x4 + 8x5) = 8x3 + 6x2 + 15x + 6 6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + (20x4 * -1 + 8x5 * -1) = 8x3 + 6x2 + 15x + 6 6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + (-20x4 + -8x5) = 8x3 + 6x2 + 15x + 6 Reorder the terms: 6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 6 + 15x + 6x2 + 8x3 Add '-6' to each side of the equation. 6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -6 + -8x5 = 6 + 15x + 6x2 + -6 + 8x3 Reorder the terms: 6 + -6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 6 + 15x + 6x2 + -6 + 8x3 Combine like terms: 6 + -6 = 0 0 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 6 + 15x + 6x2 + -6 + 8x3 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 6 + 15x + 6x2 + -6 + 8x3 Reorder the terms: 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 6 + -6 + 15x + 6x2 + 8x3 Combine like terms: 6 + -6 = 0 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 0 + 15x + 6x2 + 8x3 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 15x + 6x2 + 8x3 Add '-15x' to each side of the equation. 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -15x + -8x5 = 15x + 6x2 + -15x + 8x3 Reorder the terms: 2mx3 + 5mx4 + 2mx5 + 15x + -15x + 6x2 + -20x4 + -8x5 = 15x + 6x2 + -15x + 8x3 Combine like terms: 15x + -15x = 0 2mx3 + 5mx4 + 2mx5 + 0 + 6x2 + -20x4 + -8x5 = 15x + 6x2 + -15x + 8x3 2mx3 + 5mx4 + 2mx5 + 6x2 + -20x4 + -8x5 = 15x + 6x2 + -15x + 8x3 Reorder the terms: 2mx3 + 5mx4 + 2mx5 + 6x2 + -20x4 + -8x5 = 15x + -15x + 6x2 + 8x3 Combine like terms: 15x + -15x = 0 2mx3 + 5mx4 + 2mx5 + 6x2 + -20x4 + -8x5 = 0 + 6x2 + 8x3 2mx3 + 5mx4 + 2mx5 + 6x2 + -20x4 + -8x5 = 6x2 + 8x3 Add '-6x2' to each side of the equation. 2mx3 + 5mx4 + 2mx5 + 6x2 + -20x4 + -6x2 + -8x5 = 6x2 + -6x2 + 8x3 Reorder the terms: 2mx3 + 5mx4 + 2mx5 + 6x2 + -6x2 + -20x4 + -8x5 = 6x2 + -6x2 + 8x3 Combine like terms: 6x2 + -6x2 = 0 2mx3 + 5mx4 + 2mx5 + 0 + -20x4 + -8x5 = 6x2 + -6x2 + 8x3 2mx3 + 5mx4 + 2mx5 + -20x4 + -8x5 = 6x2 + -6x2 + 8x3 Combine like terms: 6x2 + -6x2 = 0 2mx3 + 5mx4 + 2mx5 + -20x4 + -8x5 = 0 + 8x3 2mx3 + 5mx4 + 2mx5 + -20x4 + -8x5 = 8x3 Solving 2mx3 + 5mx4 + 2mx5 + -20x4 + -8x5 = 8x3 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '20x4' to each side of the equation. 2mx3 + 5mx4 + 2mx5 + -20x4 + 20x4 + -8x5 = 8x3 + 20x4 Combine like terms: -20x4 + 20x4 = 0 2mx3 + 5mx4 + 2mx5 + 0 + -8x5 = 8x3 + 20x4 2mx3 + 5mx4 + 2mx5 + -8x5 = 8x3 + 20x4 Add '8x5' to each side of the equation. 2mx3 + 5mx4 + 2mx5 + -8x5 + 8x5 = 8x3 + 20x4 + 8x5 Combine like terms: -8x5 + 8x5 = 0 2mx3 + 5mx4 + 2mx5 + 0 = 8x3 + 20x4 + 8x5 2mx3 + 5mx4 + 2mx5 = 8x3 + 20x4 + 8x5 Reorder the terms: 2mx3 + 5mx4 + 2mx5 + -8x3 + -20x4 + -8x5 = 8x3 + -8x3 + 20x4 + -20x4 + 8x5 + -8x5 Combine like terms: 8x3 + -8x3 = 0 2mx3 + 5mx4 + 2mx5 + -8x3 + -20x4 + -8x5 = 0 + 20x4 + -20x4 + 8x5 + -8x5 2mx3 + 5mx4 + 2mx5 + -8x3 + -20x4 + -8x5 = 20x4 + -20x4 + 8x5 + -8x5 Combine like terms: 20x4 + -20x4 = 0 2mx3 + 5mx4 + 2mx5 + -8x3 + -20x4 + -8x5 = 0 + 8x5 + -8x5 2mx3 + 5mx4 + 2mx5 + -8x3 + -20x4 + -8x5 = 8x5 + -8x5 Combine like terms: 8x5 + -8x5 = 0 2mx3 + 5mx4 + 2mx5 + -8x3 + -20x4 + -8x5 = 0 Factor out the Greatest Common Factor (GCF), 'x3'. x3(2m + 5mx + 2mx2 + -8 + -20x + -8x2) = 0Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing m to the left, all other terms to the right. Add '-1x3' to each side of the equation. x3 + -1x3 = 0 + -1x3 Remove the zero: 0 = -1x3 Simplifying 0 = -1x3 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 '(2m + 5mx + 2mx2 + -8 + -20x + -8x2)' equal to zero and attempt to solve: Simplifying 2m + 5mx + 2mx2 + -8 + -20x + -8x2 = 0 Reorder the terms: -8 + 2m + 5mx + 2mx2 + -20x + -8x2 = 0 Solving -8 + 2m + 5mx + 2mx2 + -20x + -8x2 = 0 Move all terms containing m to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 2m + 5mx + 2mx2 + -20x + 8 + -8x2 = 0 + 8 Reorder the terms: -8 + 8 + 2m + 5mx + 2mx2 + -20x + -8x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 2m + 5mx + 2mx2 + -20x + -8x2 = 0 + 8 2m + 5mx + 2mx2 + -20x + -8x2 = 0 + 8 Combine like terms: 0 + 8 = 8 2m + 5mx + 2mx2 + -20x + -8x2 = 8 Add '20x' to each side of the equation. 2m + 5mx + 2mx2 + -20x + 20x + -8x2 = 8 + 20x Combine like terms: -20x + 20x = 0 2m + 5mx + 2mx2 + 0 + -8x2 = 8 + 20x 2m + 5mx + 2mx2 + -8x2 = 8 + 20x Add '8x2' to each side of the equation. 2m + 5mx + 2mx2 + -8x2 + 8x2 = 8 + 20x + 8x2 Combine like terms: -8x2 + 8x2 = 0 2m + 5mx + 2mx2 + 0 = 8 + 20x + 8x2 2m + 5mx + 2mx2 = 8 + 20x + 8x2 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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