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Simplifying 5p2 + 280 = 75p Reorder the terms: 280 + 5p2 = 75p Solving 280 + 5p2 = 75p Solving for variable 'p'. Reorder the terms: 280 + -75p + 5p2 = 75p + -75p Combine like terms: 75p + -75p = 0 280 + -75p + 5p2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(56 + -15p + p2) = 0 Factor a trinomial. 5((7 + -1p)(8 + -1p)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(7 + -1p)' equal to zero and attempt to solve: Simplifying 7 + -1p = 0 Solving 7 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1p = 0 + -7 -1p = 0 + -7 Combine like terms: 0 + -7 = -7 -1p = -7 Divide each side by '-1'. p = 7 Simplifying p = 7Subproblem 2
Set the factor '(8 + -1p)' equal to zero and attempt to solve: Simplifying 8 + -1p = 0 Solving 8 + -1p = 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 + -1p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1p = 0 + -8 -1p = 0 + -8 Combine like terms: 0 + -8 = -8 -1p = -8 Divide each side by '-1'. p = 8 Simplifying p = 8Solution
p = {7, 8}
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