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