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Simplifying 3p(5p + 2)(p + -6) = 0 Reorder the terms: 3p(2 + 5p)(p + -6) = 0 Reorder the terms: 3p(2 + 5p)(-6 + p) = 0 Multiply (2 + 5p) * (-6 + p) 3p(2(-6 + p) + 5p * (-6 + p)) = 0 3p((-6 * 2 + p * 2) + 5p * (-6 + p)) = 0 3p((-12 + 2p) + 5p * (-6 + p)) = 0 3p(-12 + 2p + (-6 * 5p + p * 5p)) = 0 3p(-12 + 2p + (-30p + 5p2)) = 0 Combine like terms: 2p + -30p = -28p 3p(-12 + -28p + 5p2) = 0 (-12 * 3p + -28p * 3p + 5p2 * 3p) = 0 (-36p + -84p2 + 15p3) = 0 Solving -36p + -84p2 + 15p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3p'. 3p(-12 + -28p + 5p2) = 0 Factor a trinomial. 3p((-2 + -5p)(6 + -1p)) = 0 Ignore the factor 3.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 '(-2 + -5p)' equal to zero and attempt to solve: Simplifying -2 + -5p = 0 Solving -2 + -5p = 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 + -5p = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5p = 0 + 2 -5p = 0 + 2 Combine like terms: 0 + 2 = 2 -5p = 2 Divide each side by '-5'. p = -0.4 Simplifying p = -0.4Subproblem 3
Set the factor '(6 + -1p)' equal to zero and attempt to solve: Simplifying 6 + -1p = 0 Solving 6 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1p = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1p = 0 + -6 -1p = 0 + -6 Combine like terms: 0 + -6 = -6 -1p = -6 Divide each side by '-1'. p = 6 Simplifying p = 6Solution
p = {0, -0.4, 6}
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