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Simplifying (p + 40)(3p + -5) = 0 Reorder the terms: (40 + p)(3p + -5) = 0 Reorder the terms: (40 + p)(-5 + 3p) = 0 Multiply (40 + p) * (-5 + 3p) (40(-5 + 3p) + p(-5 + 3p)) = 0 ((-5 * 40 + 3p * 40) + p(-5 + 3p)) = 0 ((-200 + 120p) + p(-5 + 3p)) = 0 (-200 + 120p + (-5 * p + 3p * p)) = 0 (-200 + 120p + (-5p + 3p2)) = 0 Combine like terms: 120p + -5p = 115p (-200 + 115p + 3p2) = 0 Solving -200 + 115p + 3p2 = 0 Solving for variable 'p'. Factor a trinomial. (-40 + -1p)(5 + -3p) = 0Subproblem 1
Set the factor '(-40 + -1p)' equal to zero and attempt to solve: Simplifying -40 + -1p = 0 Solving -40 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + -1p = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -1p = 0 + 40 -1p = 0 + 40 Combine like terms: 0 + 40 = 40 -1p = 40 Divide each side by '-1'. p = -40 Simplifying p = -40Subproblem 2
Set the factor '(5 + -3p)' equal to zero and attempt to solve: Simplifying 5 + -3p = 0 Solving 5 + -3p = 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 + -3p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3p = 0 + -5 -3p = 0 + -5 Combine like terms: 0 + -5 = -5 -3p = -5 Divide each side by '-3'. p = 1.666666667 Simplifying p = 1.666666667Solution
p = {-40, 1.666666667}
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