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Simplifying p(3p + 1)(3p + -1) = 0 Reorder the terms: p(1 + 3p)(3p + -1) = 0 Reorder the terms: p(1 + 3p)(-1 + 3p) = 0 Multiply (1 + 3p) * (-1 + 3p) p(1(-1 + 3p) + 3p * (-1 + 3p)) = 0 p((-1 * 1 + 3p * 1) + 3p * (-1 + 3p)) = 0 p((-1 + 3p) + 3p * (-1 + 3p)) = 0 p(-1 + 3p + (-1 * 3p + 3p * 3p)) = 0 p(-1 + 3p + (-3p + 9p2)) = 0 Combine like terms: 3p + -3p = 0 p(-1 + 0 + 9p2) = 0 p(-1 + 9p2) = 0 (-1 * p + 9p2 * p) = 0 (-1p + 9p3) = 0 Solving -1p + 9p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(-1 + 9p2) = 0 Factor a difference between two squares. p((1 + 3p)(-1 + 3p)) = 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 '(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 = -0.3333333333Subproblem 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, -0.3333333333, 0.3333333333}
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