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Simplifying (2p + 6)(p + -5) = 0 Reorder the terms: (6 + 2p)(p + -5) = 0 Reorder the terms: (6 + 2p)(-5 + p) = 0 Multiply (6 + 2p) * (-5 + p) (6(-5 + p) + 2p * (-5 + p)) = 0 ((-5 * 6 + p * 6) + 2p * (-5 + p)) = 0 ((-30 + 6p) + 2p * (-5 + p)) = 0 (-30 + 6p + (-5 * 2p + p * 2p)) = 0 (-30 + 6p + (-10p + 2p2)) = 0 Combine like terms: 6p + -10p = -4p (-30 + -4p + 2p2) = 0 Solving -30 + -4p + 2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -2p + p2) = 0 Factor a trinomial. 2((-3 + -1p)(5 + -1p)) = 0 Ignore the factor 2.Subproblem 1
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 2
Set the factor '(5 + -1p)' equal to zero and attempt to solve: Simplifying 5 + -1p = 0 Solving 5 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1p = 0 + -5 -1p = 0 + -5 Combine like terms: 0 + -5 = -5 -1p = -5 Divide each side by '-1'. p = 5 Simplifying p = 5Solution
p = {-3, 5}
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