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Simplifying F(x) = 3x2 + -6x + 0 Multiply F * x xF = 3x2 + -6x + 0 Reorder the terms: xF = 0 + -6x + 3x2 Remove the zero: xF = -6x + 3x2 Solving xF = -6x + 3x2 Solving for variable 'x'. Reorder the terms: 6x + xF + -3x2 = -6x + 3x2 + 6x + -3x2 Reorder the terms: 6x + xF + -3x2 = -6x + 6x + 3x2 + -3x2 Combine like terms: -6x + 6x = 0 6x + xF + -3x2 = 0 + 3x2 + -3x2 6x + xF + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 6x + xF + -3x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(6 + F + -3x) = 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 '(6 + F + -3x)' equal to zero and attempt to solve: Simplifying 6 + F + -3x = 0 Solving 6 + F + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + F + -6 + -3x = 0 + -6 Reorder the terms: 6 + -6 + F + -3x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + F + -3x = 0 + -6 F + -3x = 0 + -6 Combine like terms: 0 + -6 = -6 F + -3x = -6 Add '-1F' to each side of the equation. F + -1F + -3x = -6 + -1F Combine like terms: F + -1F = 0 0 + -3x = -6 + -1F -3x = -6 + -1F Divide each side by '-3'. x = 2 + 0.3333333333F Simplifying x = 2 + 0.3333333333FSolution
x = {0, 2 + 0.3333333333F}
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