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Simplifying (-3p + -1p2)(3p + 1) = 0 Reorder the terms: (-3p + -1p2)(1 + 3p) = 0 Multiply (-3p + -1p2) * (1 + 3p) (-3p * (1 + 3p) + -1p2 * (1 + 3p)) = 0 ((1 * -3p + 3p * -3p) + -1p2 * (1 + 3p)) = 0 ((-3p + -9p2) + -1p2 * (1 + 3p)) = 0 (-3p + -9p2 + (1 * -1p2 + 3p * -1p2)) = 0 (-3p + -9p2 + (-1p2 + -3p3)) = 0 Combine like terms: -9p2 + -1p2 = -10p2 (-3p + -10p2 + -3p3) = 0 Solving -3p + -10p2 + -3p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '-1p'. -1p(3 + 10p + 3p2) = 0 Factor a trinomial. -1p((3 + p)(1 + 3p)) = 0 Ignore the factor -1.Subproblem 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 '(3 + p)' equal to zero and attempt to solve: Simplifying 3 + p = 0 Solving 3 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + p = 0 + -3 p = 0 + -3 Combine like terms: 0 + -3 = -3 p = -3 Simplifying p = -3Subproblem 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, -3, -0.3333333333}
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