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Simplifying (3p + 6)(p + -4) = 0 Reorder the terms: (6 + 3p)(p + -4) = 0 Reorder the terms: (6 + 3p)(-4 + p) = 0 Multiply (6 + 3p) * (-4 + p) (6(-4 + p) + 3p * (-4 + p)) = 0 ((-4 * 6 + p * 6) + 3p * (-4 + p)) = 0 ((-24 + 6p) + 3p * (-4 + p)) = 0 (-24 + 6p + (-4 * 3p + p * 3p)) = 0 (-24 + 6p + (-12p + 3p2)) = 0 Combine like terms: 6p + -12p = -6p (-24 + -6p + 3p2) = 0 Solving -24 + -6p + 3p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + -2p + p2) = 0 Factor a trinomial. 3((-2 + -1p)(4 + -1p)) = 0 Ignore the factor 3.Subproblem 1
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 = -2Subproblem 2
Set the factor '(4 + -1p)' equal to zero and attempt to solve: Simplifying 4 + -1p = 0 Solving 4 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1p = 0 + -4 -1p = 0 + -4 Combine like terms: 0 + -4 = -4 -1p = -4 Divide each side by '-1'. p = 4 Simplifying p = 4Solution
p = {-2, 4}
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