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Simplifying F(x) = x(2x + -1)(x + 1) Multiply F * x xF = x(2x + -1)(x + 1) Reorder the terms: xF = x(-1 + 2x)(x + 1) Reorder the terms: xF = x(-1 + 2x)(1 + x) Multiply (-1 + 2x) * (1 + x) xF = x(-1(1 + x) + 2x * (1 + x)) xF = x((1 * -1 + x * -1) + 2x * (1 + x)) xF = x((-1 + -1x) + 2x * (1 + x)) xF = x(-1 + -1x + (1 * 2x + x * 2x)) xF = x(-1 + -1x + (2x + 2x2)) Combine like terms: -1x + 2x = 1x xF = x(-1 + 1x + 2x2) xF = (-1 * x + 1x * x + 2x2 * x) xF = (-1x + 1x2 + 2x3) Solving xF = -1x + 1x2 + 2x3 Solving for variable 'x'. Reorder the terms: x + xF + -1x2 + -2x3 = -1x + 1x2 + 2x3 + x + -1x2 + -2x3 Reorder the terms: x + xF + -1x2 + -2x3 = -1x + x + 1x2 + -1x2 + 2x3 + -2x3 Combine like terms: -1x + x = 0 x + xF + -1x2 + -2x3 = 0 + 1x2 + -1x2 + 2x3 + -2x3 x + xF + -1x2 + -2x3 = 1x2 + -1x2 + 2x3 + -2x3 Combine like terms: 1x2 + -1x2 = 0 x + xF + -1x2 + -2x3 = 0 + 2x3 + -2x3 x + xF + -1x2 + -2x3 = 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 x + xF + -1x2 + -2x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(1 + F + -1x + -2x2) = 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 '(1 + F + -1x + -2x2)' equal to zero and attempt to solve: Simplifying 1 + F + -1x + -2x2 = 0 Solving 1 + F + -1x + -2x2 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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