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Simplifying (p + 4)(p + 2p + -7) = 0 Reorder the terms: (4 + p)(p + 2p + -7) = 0 Reorder the terms: (4 + p)(-7 + p + 2p) = 0 Combine like terms: p + 2p = 3p (4 + p)(-7 + 3p) = 0 Multiply (4 + p) * (-7 + 3p) (4(-7 + 3p) + p(-7 + 3p)) = 0 ((-7 * 4 + 3p * 4) + p(-7 + 3p)) = 0 ((-28 + 12p) + p(-7 + 3p)) = 0 (-28 + 12p + (-7 * p + 3p * p)) = 0 (-28 + 12p + (-7p + 3p2)) = 0 Combine like terms: 12p + -7p = 5p (-28 + 5p + 3p2) = 0 Solving -28 + 5p + 3p2 = 0 Solving for variable 'p'. Factor a trinomial. (-4 + -1p)(7 + -3p) = 0Subproblem 1
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 = -4Subproblem 2
Set the factor '(7 + -3p)' equal to zero and attempt to solve: Simplifying 7 + -3p = 0 Solving 7 + -3p = 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 + -3p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3p = 0 + -7 -3p = 0 + -7 Combine like terms: 0 + -7 = -7 -3p = -7 Divide each side by '-3'. p = 2.333333333 Simplifying p = 2.333333333Solution
p = {-4, 2.333333333}
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