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Simplifying (p + -5)(p + -10) = 0 Reorder the terms: (-5 + p)(p + -10) = 0 Reorder the terms: (-5 + p)(-10 + p) = 0 Multiply (-5 + p) * (-10 + p) (-5(-10 + p) + p(-10 + p)) = 0 ((-10 * -5 + p * -5) + p(-10 + p)) = 0 ((50 + -5p) + p(-10 + p)) = 0 (50 + -5p + (-10 * p + p * p)) = 0 (50 + -5p + (-10p + p2)) = 0 Combine like terms: -5p + -10p = -15p (50 + -15p + p2) = 0 Solving 50 + -15p + p2 = 0 Solving for variable 'p'. Factor a trinomial. (5 + -1p)(10 + -1p) = 0Subproblem 1
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 = 5Subproblem 2
Set the factor '(10 + -1p)' equal to zero and attempt to solve: Simplifying 10 + -1p = 0 Solving 10 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1p = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1p = 0 + -10 -1p = 0 + -10 Combine like terms: 0 + -10 = -10 -1p = -10 Divide each side by '-1'. p = 10 Simplifying p = 10Solution
p = {5, 10}
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