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Simplifying (5p + -3)(p + -5) = 0 Reorder the terms: (-3 + 5p)(p + -5) = 0 Reorder the terms: (-3 + 5p)(-5 + p) = 0 Multiply (-3 + 5p) * (-5 + p) (-3(-5 + p) + 5p * (-5 + p)) = 0 ((-5 * -3 + p * -3) + 5p * (-5 + p)) = 0 ((15 + -3p) + 5p * (-5 + p)) = 0 (15 + -3p + (-5 * 5p + p * 5p)) = 0 (15 + -3p + (-25p + 5p2)) = 0 Combine like terms: -3p + -25p = -28p (15 + -28p + 5p2) = 0 Solving 15 + -28p + 5p2 = 0 Solving for variable 'p'. Factor a trinomial. (3 + -5p)(5 + -1p) = 0Subproblem 1
Set the factor '(3 + -5p)' equal to zero and attempt to solve: Simplifying 3 + -5p = 0 Solving 3 + -5p = 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 + -5p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5p = 0 + -3 -5p = 0 + -3 Combine like terms: 0 + -3 = -3 -5p = -3 Divide each side by '-5'. p = 0.6 Simplifying p = 0.6Subproblem 2
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 = 5Solution
p = {0.6, 5}
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