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Simplifying (4p + 3)(p + -5) = 0 Reorder the terms: (3 + 4p)(p + -5) = 0 Reorder the terms: (3 + 4p)(-5 + p) = 0 Multiply (3 + 4p) * (-5 + p) (3(-5 + p) + 4p * (-5 + p)) = 0 ((-5 * 3 + p * 3) + 4p * (-5 + p)) = 0 ((-15 + 3p) + 4p * (-5 + p)) = 0 (-15 + 3p + (-5 * 4p + p * 4p)) = 0 (-15 + 3p + (-20p + 4p2)) = 0 Combine like terms: 3p + -20p = -17p (-15 + -17p + 4p2) = 0 Solving -15 + -17p + 4p2 = 0 Solving for variable 'p'. Factor a trinomial. (-3 + -4p)(5 + -1p) = 0Subproblem 1
Set the factor '(-3 + -4p)' equal to zero and attempt to solve: Simplifying -3 + -4p = 0 Solving -3 + -4p = 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 + -4p = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4p = 0 + 3 -4p = 0 + 3 Combine like terms: 0 + 3 = 3 -4p = 3 Divide each side by '-4'. p = -0.75 Simplifying p = -0.75Subproblem 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 = {-0.75, 5}
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