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Simplifying -5p2 = 30p + 40 Reorder the terms: -5p2 = 40 + 30p Solving -5p2 = 40 + 30p Solving for variable 'p'. Reorder the terms: -40 + -30p + -5p2 = 40 + 30p + -40 + -30p Reorder the terms: -40 + -30p + -5p2 = 40 + -40 + 30p + -30p Combine like terms: 40 + -40 = 0 -40 + -30p + -5p2 = 0 + 30p + -30p -40 + -30p + -5p2 = 30p + -30p Combine like terms: 30p + -30p = 0 -40 + -30p + -5p2 = 0 Factor out the Greatest Common Factor (GCF), '-5'. -5(8 + 6p + p2) = 0 Factor a trinomial. -5((4 + p)(2 + p)) = 0 Ignore the factor -5.Subproblem 1
Set the factor '(4 + p)' equal to zero and attempt to solve: Simplifying 4 + p = 0 Solving 4 + p = 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 + p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + p = 0 + -4 p = 0 + -4 Combine like terms: 0 + -4 = -4 p = -4 Simplifying p = -4Subproblem 2
Set the factor '(2 + p)' equal to zero and attempt to solve: Simplifying 2 + p = 0 Solving 2 + p = 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 + p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + p = 0 + -2 p = 0 + -2 Combine like terms: 0 + -2 = -2 p = -2 Simplifying p = -2Solution
p = {-4, -2}
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