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Simplifying 6p3 + 8p2 = 8p Reorder the terms: 8p2 + 6p3 = 8p Solving 8p2 + 6p3 = 8p Solving for variable 'p'. Reorder the terms: -8p + 8p2 + 6p3 = 8p + -8p Combine like terms: 8p + -8p = 0 -8p + 8p2 + 6p3 = 0 Factor out the Greatest Common Factor (GCF), '2p'. 2p(-4 + 4p + 3p2) = 0 Factor a trinomial. 2p((-2 + -1p)(2 + -3p)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0Subproblem 2
Set the factor '(-2 + -1p)' equal to zero and attempt to solve: Simplifying -2 + -1p = 0 Solving -2 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1p = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1p = 0 + 2 -1p = 0 + 2 Combine like terms: 0 + 2 = 2 -1p = 2 Divide each side by '-1'. p = -2 Simplifying p = -2Subproblem 3
Set the factor '(2 + -3p)' equal to zero and attempt to solve: Simplifying 2 + -3p = 0 Solving 2 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3p = 0 + -2 -3p = 0 + -2 Combine like terms: 0 + -2 = -2 -3p = -2 Divide each side by '-3'. p = 0.6666666667 Simplifying p = 0.6666666667Solution
p = {0, -2, 0.6666666667}
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