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Simplifying 15p4 + 8p2 = -26p3 Reorder the terms: 8p2 + 15p4 = -26p3 Solving 8p2 + 15p4 = -26p3 Solving for variable 'p'. Reorder the terms: 8p2 + 26p3 + 15p4 = -26p3 + 26p3 Combine like terms: -26p3 + 26p3 = 0 8p2 + 26p3 + 15p4 = 0 Factor out the Greatest Common Factor (GCF), 'p2'. p2(8 + 26p + 15p2) = 0 Factor a trinomial. p2((4 + 3p)(2 + 5p)) = 0Subproblem 1
Set the factor 'p2' equal to zero and attempt to solve: Simplifying p2 = 0 Solving p2 = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p2 = 0 Take the square root of each side: p = {0}Subproblem 2
Set the factor '(4 + 3p)' equal to zero and attempt to solve: Simplifying 4 + 3p = 0 Solving 4 + 3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3p = 0 + -4 3p = 0 + -4 Combine like terms: 0 + -4 = -4 3p = -4 Divide each side by '3'. p = -1.333333333 Simplifying p = -1.333333333Subproblem 3
Set the factor '(2 + 5p)' equal to zero and attempt to solve: Simplifying 2 + 5p = 0 Solving 2 + 5p = 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 + 5p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5p = 0 + -2 5p = 0 + -2 Combine like terms: 0 + -2 = -2 5p = -2 Divide each side by '5'. p = -0.4 Simplifying p = -0.4Solution
p = {0, -1.333333333, -0.4}
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