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Simplifying (4p + -5)(p + -2) = 0 Reorder the terms: (-5 + 4p)(p + -2) = 0 Reorder the terms: (-5 + 4p)(-2 + p) = 0 Multiply (-5 + 4p) * (-2 + p) (-5(-2 + p) + 4p * (-2 + p)) = 0 ((-2 * -5 + p * -5) + 4p * (-2 + p)) = 0 ((10 + -5p) + 4p * (-2 + p)) = 0 (10 + -5p + (-2 * 4p + p * 4p)) = 0 (10 + -5p + (-8p + 4p2)) = 0 Combine like terms: -5p + -8p = -13p (10 + -13p + 4p2) = 0 Solving 10 + -13p + 4p2 = 0 Solving for variable 'p'. Factor a trinomial. (5 + -4p)(2 + -1p) = 0Subproblem 1
Set the factor '(5 + -4p)' equal to zero and attempt to solve: Simplifying 5 + -4p = 0 Solving 5 + -4p = 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 + -4p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4p = 0 + -5 -4p = 0 + -5 Combine like terms: 0 + -5 = -5 -4p = -5 Divide each side by '-4'. p = 1.25 Simplifying p = 1.25Subproblem 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 = {1.25, 2}
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