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Simplifying (-2p + 5)(-8p + 3) = 0 Reorder the terms: (5 + -2p)(-8p + 3) = 0 Reorder the terms: (5 + -2p)(3 + -8p) = 0 Multiply (5 + -2p) * (3 + -8p) (5(3 + -8p) + -2p * (3 + -8p)) = 0 ((3 * 5 + -8p * 5) + -2p * (3 + -8p)) = 0 ((15 + -40p) + -2p * (3 + -8p)) = 0 (15 + -40p + (3 * -2p + -8p * -2p)) = 0 (15 + -40p + (-6p + 16p2)) = 0 Combine like terms: -40p + -6p = -46p (15 + -46p + 16p2) = 0 Solving 15 + -46p + 16p2 = 0 Solving for variable 'p'. Factor a trinomial. (3 + -8p)(5 + -2p) = 0Subproblem 1
Set the factor '(3 + -8p)' equal to zero and attempt to solve: Simplifying 3 + -8p = 0 Solving 3 + -8p = 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 + -8p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8p = 0 + -3 -8p = 0 + -3 Combine like terms: 0 + -3 = -3 -8p = -3 Divide each side by '-8'. p = 0.375 Simplifying p = 0.375Subproblem 2
Set the factor '(5 + -2p)' equal to zero and attempt to solve: Simplifying 5 + -2p = 0 Solving 5 + -2p = 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 + -2p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2p = 0 + -5 -2p = 0 + -5 Combine like terms: 0 + -5 = -5 -2p = -5 Divide each side by '-2'. p = 2.5 Simplifying p = 2.5Solution
p = {0.375, 2.5}
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