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Simplifying (mx + 3)(4x + -2) + -1(2x + -4) = 0 Reorder the terms: (3 + mx)(4x + -2) + -1(2x + -4) = 0 Reorder the terms: (3 + mx)(-2 + 4x) + -1(2x + -4) = 0 Multiply (3 + mx) * (-2 + 4x) (3(-2 + 4x) + mx(-2 + 4x)) + -1(2x + -4) = 0 ((-2 * 3 + 4x * 3) + mx(-2 + 4x)) + -1(2x + -4) = 0 ((-6 + 12x) + mx(-2 + 4x)) + -1(2x + -4) = 0 (-6 + 12x + (-2 * mx + 4x * mx)) + -1(2x + -4) = 0 (-6 + 12x + (-2mx + 4mx2)) + -1(2x + -4) = 0 Reorder the terms: (-6 + -2mx + 4mx2 + 12x) + -1(2x + -4) = 0 (-6 + -2mx + 4mx2 + 12x) + -1(2x + -4) = 0 Reorder the terms: -6 + -2mx + 4mx2 + 12x + -1(-4 + 2x) = 0 -6 + -2mx + 4mx2 + 12x + (-4 * -1 + 2x * -1) = 0 -6 + -2mx + 4mx2 + 12x + (4 + -2x) = 0 Reorder the terms: -6 + 4 + -2mx + 4mx2 + 12x + -2x = 0 Combine like terms: -6 + 4 = -2 -2 + -2mx + 4mx2 + 12x + -2x = 0 Combine like terms: 12x + -2x = 10x -2 + -2mx + 4mx2 + 10x = 0 Solving -2 + -2mx + 4mx2 + 10x = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + -2mx + 4mx2 + 2 + 10x = 0 + 2 Reorder the terms: -2 + 2 + -2mx + 4mx2 + 10x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2mx + 4mx2 + 10x = 0 + 2 -2mx + 4mx2 + 10x = 0 + 2 Combine like terms: 0 + 2 = 2 -2mx + 4mx2 + 10x = 2 Add '-10x' to each side of the equation. -2mx + 4mx2 + 10x + -10x = 2 + -10x Combine like terms: 10x + -10x = 0 -2mx + 4mx2 + 0 = 2 + -10x -2mx + 4mx2 = 2 + -10x Reorder the terms: -2 + -2mx + 4mx2 + 10x = 2 + -10x + -2 + 10x Reorder the terms: -2 + -2mx + 4mx2 + 10x = 2 + -2 + -10x + 10x Combine like terms: 2 + -2 = 0 -2 + -2mx + 4mx2 + 10x = 0 + -10x + 10x -2 + -2mx + 4mx2 + 10x = -10x + 10x Combine like terms: -10x + 10x = 0 -2 + -2mx + 4mx2 + 10x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -1mx + 2mx2 + 5x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -1mx + 2mx2 + 5x)' equal to zero and attempt to solve: Simplifying -1 + -1mx + 2mx2 + 5x = 0 Solving -1 + -1mx + 2mx2 + 5x = 0 Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -1mx + 2mx2 + 1 + 5x = 0 + 1 Reorder the terms: -1 + 1 + -1mx + 2mx2 + 5x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1mx + 2mx2 + 5x = 0 + 1 -1mx + 2mx2 + 5x = 0 + 1 Combine like terms: 0 + 1 = 1 -1mx + 2mx2 + 5x = 1 Add '-5x' to each side of the equation. -1mx + 2mx2 + 5x + -5x = 1 + -5x Combine like terms: 5x + -5x = 0 -1mx + 2mx2 + 0 = 1 + -5x -1mx + 2mx2 = 1 + -5x 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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