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Simplifying 5p(p + 3)(p + -2) = 0 Reorder the terms: 5p(3 + p)(p + -2) = 0 Reorder the terms: 5p(3 + p)(-2 + p) = 0 Multiply (3 + p) * (-2 + p) 5p(3(-2 + p) + p(-2 + p)) = 0 5p((-2 * 3 + p * 3) + p(-2 + p)) = 0 5p((-6 + 3p) + p(-2 + p)) = 0 5p(-6 + 3p + (-2 * p + p * p)) = 0 5p(-6 + 3p + (-2p + p2)) = 0 Combine like terms: 3p + -2p = 1p 5p(-6 + 1p + p2) = 0 (-6 * 5p + 1p * 5p + p2 * 5p) = 0 (-30p + 5p2 + 5p3) = 0 Solving -30p + 5p2 + 5p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '5p'. 5p(-6 + p + p2) = 0 Factor a trinomial. 5p((-3 + -1p)(2 + -1p)) = 0 Ignore the factor 5.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 + -1p)' equal to zero and attempt to solve: Simplifying -3 + -1p = 0 Solving -3 + -1p = 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 + -1p = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1p = 0 + 3 -1p = 0 + 3 Combine like terms: 0 + 3 = 3 -1p = 3 Divide each side by '-1'. p = -3 Simplifying p = -3Subproblem 3
Set the factor '(2 + -1p)' equal to zero and attempt to solve: Simplifying 2 + -1p = 0 Solving 2 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1p = 0 + -2 -1p = 0 + -2 Combine like terms: 0 + -2 = -2 -1p = -2 Divide each side by '-1'. p = 2 Simplifying p = 2Solution
p = {0, -3, 2}
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