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Simplifying p3 + -81p = 0 Reorder the terms: -81p + p3 = 0 Solving -81p + p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(-81 + p2) = 0 Factor a difference between two squares. p((9 + p)(-9 + p)) = 0Subproblem 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 '(9 + p)' equal to zero and attempt to solve: Simplifying 9 + p = 0 Solving 9 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + p = 0 + -9 Combine like terms: 9 + -9 = 0 0 + p = 0 + -9 p = 0 + -9 Combine like terms: 0 + -9 = -9 p = -9 Simplifying p = -9Subproblem 3
Set the factor '(-9 + p)' equal to zero and attempt to solve: Simplifying -9 + p = 0 Solving -9 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + p = 0 + 9 Combine like terms: -9 + 9 = 0 0 + p = 0 + 9 p = 0 + 9 Combine like terms: 0 + 9 = 9 p = 9 Simplifying p = 9Solution
p = {0, -9, 9}
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