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Simplifying 3x(2x + -3) = x(x + 1) Reorder the terms: 3x(-3 + 2x) = x(x + 1) (-3 * 3x + 2x * 3x) = x(x + 1) (-9x + 6x2) = x(x + 1) Reorder the terms: -9x + 6x2 = x(1 + x) -9x + 6x2 = (1 * x + x * x) -9x + 6x2 = (1x + x2) Solving -9x + 6x2 = 1x + x2 Solving for variable 'x'. Reorder the terms: -9x + -1x + 6x2 + -1x2 = 1x + x2 + -1x + -1x2 Combine like terms: -9x + -1x = -10x -10x + 6x2 + -1x2 = 1x + x2 + -1x + -1x2 Combine like terms: 6x2 + -1x2 = 5x2 -10x + 5x2 = 1x + x2 + -1x + -1x2 Reorder the terms: -10x + 5x2 = 1x + -1x + x2 + -1x2 Combine like terms: 1x + -1x = 0 -10x + 5x2 = 0 + x2 + -1x2 -10x + 5x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -10x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5x'. 5x(-2 + x) = 0 Ignore the factor 5.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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