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Simplifying (5p + 3)(3p + -8) = 0 Reorder the terms: (3 + 5p)(3p + -8) = 0 Reorder the terms: (3 + 5p)(-8 + 3p) = 0 Multiply (3 + 5p) * (-8 + 3p) (3(-8 + 3p) + 5p * (-8 + 3p)) = 0 ((-8 * 3 + 3p * 3) + 5p * (-8 + 3p)) = 0 ((-24 + 9p) + 5p * (-8 + 3p)) = 0 (-24 + 9p + (-8 * 5p + 3p * 5p)) = 0 (-24 + 9p + (-40p + 15p2)) = 0 Combine like terms: 9p + -40p = -31p (-24 + -31p + 15p2) = 0 Solving -24 + -31p + 15p2 = 0 Solving for variable 'p'. Factor a trinomial. (-3 + -5p)(8 + -3p) = 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 '(8 + -3p)' equal to zero and attempt to solve: Simplifying 8 + -3p = 0 Solving 8 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3p = 0 + -8 -3p = 0 + -8 Combine like terms: 0 + -8 = -8 -3p = -8 Divide each side by '-3'. p = 2.666666667 Simplifying p = 2.666666667Solution
p = {-0.6, 2.666666667}
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