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Simplifying (p * p * p) + -1(1p * 2p) = (p * p) + 40p Multiply p * p (p2 * p) + -1(1p * 2p) = (p * p) + 40p Multiply p2 * p (p3) + -1(1p * 2p) = (p * p) + 40p p3 + -1(1p * 2p) = (p * p) + 40p Reorder the terms for easier multiplication: p3 + -1(1 * 2p * p) = (p * p) + 40p Multiply 1 * 2 p3 + -1(2p * p) = (p * p) + 40p Multiply p * p p3 + -1(2p2) = (p * p) + 40p Remove parenthesis around (2p2) p3 + -1 * 2p2 = (p * p) + 40p Multiply -1 * 2 p3 + -2p2 = (p * p) + 40p Reorder the terms: -2p2 + p3 = (p * p) + 40p Multiply p * p -2p2 + p3 = (p2) + 40p -2p2 + p3 = p2 + 40p Reorder the terms: -2p2 + p3 = 40p + p2 Solving -2p2 + p3 = 40p + p2 Solving for variable 'p'. Reorder the terms: -40p + -2p2 + -1p2 + p3 = 40p + p2 + -40p + -1p2 Combine like terms: -2p2 + -1p2 = -3p2 -40p + -3p2 + p3 = 40p + p2 + -40p + -1p2 Reorder the terms: -40p + -3p2 + p3 = 40p + -40p + p2 + -1p2 Combine like terms: 40p + -40p = 0 -40p + -3p2 + p3 = 0 + p2 + -1p2 -40p + -3p2 + p3 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 -40p + -3p2 + p3 = 0 Factor out the Greatest Common Factor (GCF), 'p'. p(-40 + -3p + p2) = 0 Factor a trinomial. p((-5 + -1p)(8 + -1p)) = 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 '(-5 + -1p)' equal to zero and attempt to solve: Simplifying -5 + -1p = 0 Solving -5 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1p = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1p = 0 + 5 -1p = 0 + 5 Combine like terms: 0 + 5 = 5 -1p = 5 Divide each side by '-1'. p = -5 Simplifying p = -5Subproblem 3
Set the factor '(8 + -1p)' equal to zero and attempt to solve: Simplifying 8 + -1p = 0 Solving 8 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1p = 0 + -8 -1p = 0 + -8 Combine like terms: 0 + -8 = -8 -1p = -8 Divide each side by '-1'. p = 8 Simplifying p = 8Solution
p = {0, -5, 8}
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