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Simplifying 4p2 = -12p + 40 Reorder the terms: 4p2 = 40 + -12p Solving 4p2 = 40 + -12p Solving for variable 'p'. Reorder the terms: -40 + 12p + 4p2 = 40 + -12p + -40 + 12p Reorder the terms: -40 + 12p + 4p2 = 40 + -40 + -12p + 12p Combine like terms: 40 + -40 = 0 -40 + 12p + 4p2 = 0 + -12p + 12p -40 + 12p + 4p2 = -12p + 12p Combine like terms: -12p + 12p = 0 -40 + 12p + 4p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + 3p + p2) = 0 Factor a trinomial. 4((-5 + -1p)(2 + -1p)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -1p)' equal to zero and attempt to solve: Simplifying -5 + -1p = 0 Solving -5 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1p = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1p = 0 + 5 -1p = 0 + 5 Combine like terms: 0 + 5 = 5 -1p = 5 Divide each side by '-1'. p = -5 Simplifying p = -5Subproblem 2
Set the factor '(2 + -1p)' equal to zero and attempt to solve: Simplifying 2 + -1p = 0 Solving 2 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1p = 0 + -2 -1p = 0 + -2 Combine like terms: 0 + -2 = -2 -1p = -2 Divide each side by '-1'. p = 2 Simplifying p = 2Solution
p = {-5, 2}
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