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Simplifying 6p2 + 252 = 78p Reorder the terms: 252 + 6p2 = 78p Solving 252 + 6p2 = 78p Solving for variable 'p'. Reorder the terms: 252 + -78p + 6p2 = 78p + -78p Combine like terms: 78p + -78p = 0 252 + -78p + 6p2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(42 + -13p + p2) = 0 Factor a trinomial. 6((6 + -1p)(7 + -1p)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(6 + -1p)' equal to zero and attempt to solve: Simplifying 6 + -1p = 0 Solving 6 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1p = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1p = 0 + -6 -1p = 0 + -6 Combine like terms: 0 + -6 = -6 -1p = -6 Divide each side by '-1'. p = 6 Simplifying p = 6Subproblem 2
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 = 7Solution
p = {6, 7}
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