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Simplifying x(3x + -5) = 4x + -1(5 + -1x) * x Reorder the terms: x(-5 + 3x) = 4x + -1(5 + -1x) * x (-5 * x + 3x * x) = 4x + -1(5 + -1x) * x (-5x + 3x2) = 4x + -1(5 + -1x) * x Reorder the terms for easier multiplication: -5x + 3x2 = 4x + -1x(5 + -1x) -5x + 3x2 = 4x + (5 * -1x + -1x * -1x) -5x + 3x2 = 4x + (-5x + 1x2) Combine like terms: 4x + -5x = -1x -5x + 3x2 = -1x + 1x2 Solving -5x + 3x2 = -1x + 1x2 Solving for variable 'x'. Reorder the terms: -5x + x + 3x2 + -1x2 = -1x + 1x2 + x + -1x2 Combine like terms: -5x + x = -4x -4x + 3x2 + -1x2 = -1x + 1x2 + x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -4x + 2x2 = -1x + 1x2 + x + -1x2 Reorder the terms: -4x + 2x2 = -1x + x + 1x2 + -1x2 Combine like terms: -1x + x = 0 -4x + 2x2 = 0 + 1x2 + -1x2 -4x + 2x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-2 + x) = 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 x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Solution
x = {0, 2}
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