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Simplifying 5p2 + 12p = 32 Reorder the terms: 12p + 5p2 = 32 Solving 12p + 5p2 = 32 Solving for variable 'p'. Reorder the terms: -32 + 12p + 5p2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 12p + 5p2 = 0 Factor a trinomial. (-4 + -1p)(8 + -5p) = 0Subproblem 1
Set the factor '(-4 + -1p)' equal to zero and attempt to solve: Simplifying -4 + -1p = 0 Solving -4 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1p = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1p = 0 + 4 -1p = 0 + 4 Combine like terms: 0 + 4 = 4 -1p = 4 Divide each side by '-1'. p = -4 Simplifying p = -4Subproblem 2
Set the factor '(8 + -5p)' equal to zero and attempt to solve: Simplifying 8 + -5p = 0 Solving 8 + -5p = 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 + -5p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5p = 0 + -8 -5p = 0 + -8 Combine like terms: 0 + -8 = -8 -5p = -8 Divide each side by '-5'. p = 1.6 Simplifying p = 1.6Solution
p = {-4, 1.6}
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