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Simplifying -1x3 + x + -1 = (1 + -1x)(3x2 + -1) Reorder the terms: -1 + x + -1x3 = (1 + -1x)(3x2 + -1) Reorder the terms: -1 + x + -1x3 = (1 + -1x)(-1 + 3x2) Multiply (1 + -1x) * (-1 + 3x2) -1 + x + -1x3 = (1(-1 + 3x2) + -1x * (-1 + 3x2)) -1 + x + -1x3 = ((-1 * 1 + 3x2 * 1) + -1x * (-1 + 3x2)) -1 + x + -1x3 = ((-1 + 3x2) + -1x * (-1 + 3x2)) -1 + x + -1x3 = (-1 + 3x2 + (-1 * -1x + 3x2 * -1x)) -1 + x + -1x3 = (-1 + 3x2 + (1x + -3x3)) Reorder the terms: -1 + x + -1x3 = (-1 + 1x + 3x2 + -3x3) -1 + x + -1x3 = (-1 + 1x + 3x2 + -3x3) Add '1' to each side of the equation. -1 + x + 1 + -1x3 = -1 + 1x + 3x2 + 1 + -3x3 Reorder the terms: -1 + 1 + x + -1x3 = -1 + 1x + 3x2 + 1 + -3x3 Combine like terms: -1 + 1 = 0 0 + x + -1x3 = -1 + 1x + 3x2 + 1 + -3x3 x + -1x3 = -1 + 1x + 3x2 + 1 + -3x3 Reorder the terms: x + -1x3 = -1 + 1 + 1x + 3x2 + -3x3 Combine like terms: -1 + 1 = 0 x + -1x3 = 0 + 1x + 3x2 + -3x3 x + -1x3 = 1x + 3x2 + -3x3 Solving x + -1x3 = 1x + 3x2 + -3x3 Solving for variable 'x'. Reorder the terms: x + -1x + -3x2 + -1x3 + 3x3 = 1x + 3x2 + -3x3 + -1x + -3x2 + 3x3 Combine like terms: x + -1x = 0 0 + -3x2 + -1x3 + 3x3 = 1x + 3x2 + -3x3 + -1x + -3x2 + 3x3 -3x2 + -1x3 + 3x3 = 1x + 3x2 + -3x3 + -1x + -3x2 + 3x3 Combine like terms: -1x3 + 3x3 = 2x3 -3x2 + 2x3 = 1x + 3x2 + -3x3 + -1x + -3x2 + 3x3 Reorder the terms: -3x2 + 2x3 = 1x + -1x + 3x2 + -3x2 + -3x3 + 3x3 Combine like terms: 1x + -1x = 0 -3x2 + 2x3 = 0 + 3x2 + -3x2 + -3x3 + 3x3 -3x2 + 2x3 = 3x2 + -3x2 + -3x3 + 3x3 Combine like terms: 3x2 + -3x2 = 0 -3x2 + 2x3 = 0 + -3x3 + 3x3 -3x2 + 2x3 = -3x3 + 3x3 Combine like terms: -3x3 + 3x3 = 0 -3x2 + 2x3 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-3 + 2x) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 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 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Divide each side by '2'. x = 1.5 Simplifying x = 1.5Solution
x = {0, 1.5}
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