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Simplifying 51p2 + 36p3 = 21p Solving 51p2 + 36p3 = 21p Solving for variable 'p'. Reorder the terms: -21p + 51p2 + 36p3 = 21p + -21p Combine like terms: 21p + -21p = 0 -21p + 51p2 + 36p3 = 0 Factor out the Greatest Common Factor (GCF), '3p'. 3p(-7 + 17p + 12p2) = 0 Factor a trinomial. 3p((-7 + -4p)(1 + -3p)) = 0 Ignore the factor 3.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 '(-7 + -4p)' equal to zero and attempt to solve: Simplifying -7 + -4p = 0 Solving -7 + -4p = 0 Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -4p = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4p = 0 + 7 -4p = 0 + 7 Combine like terms: 0 + 7 = 7 -4p = 7 Divide each side by '-4'. p = -1.75 Simplifying p = -1.75Subproblem 3
Set the factor '(1 + -3p)' equal to zero and attempt to solve: Simplifying 1 + -3p = 0 Solving 1 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3p = 0 + -1 -3p = 0 + -1 Combine like terms: 0 + -1 = -1 -3p = -1 Divide each side by '-3'. p = 0.3333333333 Simplifying p = 0.3333333333Solution
p = {0, -1.75, 0.3333333333}
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