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Simplifying (7p + -14)(8 + -2p) = 0 Reorder the terms: (-14 + 7p)(8 + -2p) = 0 Multiply (-14 + 7p) * (8 + -2p) (-14(8 + -2p) + 7p * (8 + -2p)) = 0 ((8 * -14 + -2p * -14) + 7p * (8 + -2p)) = 0 ((-112 + 28p) + 7p * (8 + -2p)) = 0 (-112 + 28p + (8 * 7p + -2p * 7p)) = 0 (-112 + 28p + (56p + -14p2)) = 0 Combine like terms: 28p + 56p = 84p (-112 + 84p + -14p2) = 0 Solving -112 + 84p + -14p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '14'. 14(-8 + 6p + -1p2) = 0 Factor a trinomial. 14((-4 + p)(2 + -1p)) = 0 Ignore the factor 14.Subproblem 1
Set the factor '(-4 + p)' equal to zero and attempt to solve: Simplifying -4 + p = 0 Solving -4 + p = 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 + p = 0 + 4 Combine like terms: -4 + 4 = 0 0 + p = 0 + 4 p = 0 + 4 Combine like terms: 0 + 4 = 4 p = 4 Simplifying p = 4Subproblem 2
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 = 2Solution
p = {4, 2}
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