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Simplifying f(x) = 2x3 + -6xf(x + 1) Multiply f * x fx = 2x3 + -6xf(x + 1) Reorder the terms: fx = 2x3 + -6fx(1 + x) fx = 2x3 + (1 * -6fx + x * -6fx) fx = 2x3 + (-6fx + -6fx2) Reorder the terms: fx = -6fx + -6fx2 + 2x3 Solving fx = -6fx + -6fx2 + 2x3 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '6fx' to each side of the equation. fx + 6fx = -6fx + -6fx2 + 6fx + 2x3 Combine like terms: fx + 6fx = 7fx 7fx = -6fx + -6fx2 + 6fx + 2x3 Reorder the terms: 7fx = -6fx + 6fx + -6fx2 + 2x3 Combine like terms: -6fx + 6fx = 0 7fx = 0 + -6fx2 + 2x3 7fx = -6fx2 + 2x3 Add '6fx2' to each side of the equation. 7fx + 6fx2 = -6fx2 + 6fx2 + 2x3 Combine like terms: -6fx2 + 6fx2 = 0 7fx + 6fx2 = 0 + 2x3 7fx + 6fx2 = 2x3 Combine like terms: 2x3 + -2x3 = 0 7fx + 6fx2 + -2x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(7f + 6fx + -2x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing f to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(7f + 6fx + -2x2)' equal to zero and attempt to solve: Simplifying 7f + 6fx + -2x2 = 0 Solving 7f + 6fx + -2x2 = 0 Move all terms containing f to the left, all other terms to the right. Add '2x2' to each side of the equation. 7f + 6fx + -2x2 + 2x2 = 0 + 2x2 Combine like terms: -2x2 + 2x2 = 0 7f + 6fx + 0 = 0 + 2x2 7f + 6fx = 0 + 2x2 Remove the zero: 7f + 6fx = 2x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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