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Simplifying 6p2 + 15p + -63 = 3p + 3p2 Reorder the terms: -63 + 15p + 6p2 = 3p + 3p2 Solving -63 + 15p + 6p2 = 3p + 3p2 Solving for variable 'p'. Reorder the terms: -63 + 15p + -3p + 6p2 + -3p2 = 3p + 3p2 + -3p + -3p2 Combine like terms: 15p + -3p = 12p -63 + 12p + 6p2 + -3p2 = 3p + 3p2 + -3p + -3p2 Combine like terms: 6p2 + -3p2 = 3p2 -63 + 12p + 3p2 = 3p + 3p2 + -3p + -3p2 Reorder the terms: -63 + 12p + 3p2 = 3p + -3p + 3p2 + -3p2 Combine like terms: 3p + -3p = 0 -63 + 12p + 3p2 = 0 + 3p2 + -3p2 -63 + 12p + 3p2 = 3p2 + -3p2 Combine like terms: 3p2 + -3p2 = 0 -63 + 12p + 3p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-21 + 4p + p2) = 0 Factor a trinomial. 3((-7 + -1p)(3 + -1p)) = 0 Ignore the factor 3.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 '(3 + -1p)' equal to zero and attempt to solve: Simplifying 3 + -1p = 0 Solving 3 + -1p = 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 + -1p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1p = 0 + -3 -1p = 0 + -3 Combine like terms: 0 + -3 = -3 -1p = -3 Divide each side by '-1'. p = 3 Simplifying p = 3Solution
p = {-7, 3}
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