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Simplifying -2p2 = 9p3 + -5p2 Reorder the terms: -2p2 = -5p2 + 9p3 Solving -2p2 = -5p2 + 9p3 Solving for variable 'p'. Combine like terms: -2p2 + 5p2 = 3p2 3p2 + -9p3 = -5p2 + 9p3 + 5p2 + -9p3 Reorder the terms: 3p2 + -9p3 = -5p2 + 5p2 + 9p3 + -9p3 Combine like terms: -5p2 + 5p2 = 0 3p2 + -9p3 = 0 + 9p3 + -9p3 3p2 + -9p3 = 9p3 + -9p3 Combine like terms: 9p3 + -9p3 = 0 3p2 + -9p3 = 0 Factor out the Greatest Common Factor (GCF), '3p2'. 3p2(1 + -3p) = 0 Ignore the factor 3.Subproblem 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 '(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, 0.3333333333}
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