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Simplifying (p + 3)(-6p + -8) = 0 Reorder the terms: (3 + p)(-6p + -8) = 0 Reorder the terms: (3 + p)(-8 + -6p) = 0 Multiply (3 + p) * (-8 + -6p) (3(-8 + -6p) + p(-8 + -6p)) = 0 ((-8 * 3 + -6p * 3) + p(-8 + -6p)) = 0 ((-24 + -18p) + p(-8 + -6p)) = 0 (-24 + -18p + (-8 * p + -6p * p)) = 0 (-24 + -18p + (-8p + -6p2)) = 0 Combine like terms: -18p + -8p = -26p (-24 + -26p + -6p2) = 0 Solving -24 + -26p + -6p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '-2'. -2(12 + 13p + 3p2) = 0 Factor a trinomial. -2((3 + p)(4 + 3p)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(3 + p)' equal to zero and attempt to solve: Simplifying 3 + p = 0 Solving 3 + p = 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 + p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + p = 0 + -3 p = 0 + -3 Combine like terms: 0 + -3 = -3 p = -3 Simplifying p = -3Subproblem 2
Set the factor '(4 + 3p)' equal to zero and attempt to solve: Simplifying 4 + 3p = 0 Solving 4 + 3p = 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 + 3p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3p = 0 + -4 3p = 0 + -4 Combine like terms: 0 + -4 = -4 3p = -4 Divide each side by '3'. p = -1.333333333 Simplifying p = -1.333333333Solution
p = {-3, -1.333333333}
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