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Simplifying (p + 3)(p + -5) + -2(p + 3) = 0 Reorder the terms: (3 + p)(p + -5) + -2(p + 3) = 0 Reorder the terms: (3 + p)(-5 + p) + -2(p + 3) = 0 Multiply (3 + p) * (-5 + p) (3(-5 + p) + p(-5 + p)) + -2(p + 3) = 0 ((-5 * 3 + p * 3) + p(-5 + p)) + -2(p + 3) = 0 ((-15 + 3p) + p(-5 + p)) + -2(p + 3) = 0 (-15 + 3p + (-5 * p + p * p)) + -2(p + 3) = 0 (-15 + 3p + (-5p + p2)) + -2(p + 3) = 0 Combine like terms: 3p + -5p = -2p (-15 + -2p + p2) + -2(p + 3) = 0 Reorder the terms: -15 + -2p + p2 + -2(3 + p) = 0 -15 + -2p + p2 + (3 * -2 + p * -2) = 0 -15 + -2p + p2 + (-6 + -2p) = 0 Reorder the terms: -15 + -6 + -2p + -2p + p2 = 0 Combine like terms: -15 + -6 = -21 -21 + -2p + -2p + p2 = 0 Combine like terms: -2p + -2p = -4p -21 + -4p + p2 = 0 Solving -21 + -4p + p2 = 0 Solving for variable 'p'. Factor a trinomial. (-3 + -1p)(7 + -1p) = 0Subproblem 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 '(7 + -1p)' equal to zero and attempt to solve: Simplifying 7 + -1p = 0 Solving 7 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1p = 0 + -7 -1p = 0 + -7 Combine like terms: 0 + -7 = -7 -1p = -7 Divide each side by '-1'. p = 7 Simplifying p = 7Solution
p = {-3, 7}
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