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Simplifying 4p(2pf + -1p + -1f) = 0 Reorder the terms: 4p(-1f + 2fp + -1p) = 0 (-1f * 4p + 2fp * 4p + -1p * 4p) = 0 (-4fp + 8fp2 + -4p2) = 0 Solving -4fp + 8fp2 + -4p2 = 0 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '4p2' to each side of the equation. -4fp + 8fp2 + -4p2 + 4p2 = 0 + 4p2 Combine like terms: -4p2 + 4p2 = 0 -4fp + 8fp2 + 0 = 0 + 4p2 -4fp + 8fp2 = 0 + 4p2 Remove the zero: -4fp + 8fp2 = 4p2 Combine like terms: 4p2 + -4p2 = 0 -4fp + 8fp2 + -4p2 = 0 Factor out the Greatest Common Factor (GCF), '4p'. 4p(-1f + 2fp + -1p) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing f to the left, all other terms to the right. Add '-1p' to each side of the equation. p + -1p = 0 + -1p Remove the zero: 0 = -1p Simplifying 0 = -1p 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 '(-1f + 2fp + -1p)' equal to zero and attempt to solve: Simplifying -1f + 2fp + -1p = 0 Solving -1f + 2fp + -1p = 0 Move all terms containing f to the left, all other terms to the right. Add 'p' to each side of the equation. -1f + 2fp + -1p + p = 0 + p Combine like terms: -1p + p = 0 -1f + 2fp + 0 = 0 + p -1f + 2fp = 0 + p Remove the zero: -1f + 2fp = p 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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