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Simplifying 0 = (3p + 5)(3p + 5) Reorder the terms: 0 = (5 + 3p)(3p + 5) Reorder the terms: 0 = (5 + 3p)(5 + 3p) Multiply (5 + 3p) * (5 + 3p) 0 = (5(5 + 3p) + 3p * (5 + 3p)) 0 = ((5 * 5 + 3p * 5) + 3p * (5 + 3p)) 0 = ((25 + 15p) + 3p * (5 + 3p)) 0 = (25 + 15p + (5 * 3p + 3p * 3p)) 0 = (25 + 15p + (15p + 9p2)) Combine like terms: 15p + 15p = 30p 0 = (25 + 30p + 9p2) Solving 0 = 25 + 30p + 9p2 Solving for variable 'p'. Combine like terms: 0 + -25 = -25 -25 + -30p + -9p2 = 25 + 30p + 9p2 + -25 + -30p + -9p2 Reorder the terms: -25 + -30p + -9p2 = 25 + -25 + 30p + -30p + 9p2 + -9p2 Combine like terms: 25 + -25 = 0 -25 + -30p + -9p2 = 0 + 30p + -30p + 9p2 + -9p2 -25 + -30p + -9p2 = 30p + -30p + 9p2 + -9p2 Combine like terms: 30p + -30p = 0 -25 + -30p + -9p2 = 0 + 9p2 + -9p2 -25 + -30p + -9p2 = 9p2 + -9p2 Combine like terms: 9p2 + -9p2 = 0 -25 + -30p + -9p2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(25 + 30p + 9p2) = 0 Factor a trinomial. -1((5 + 3p)(5 + 3p)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 3p)' equal to zero and attempt to solve: Simplifying 5 + 3p = 0 Solving 5 + 3p = 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 + 3p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3p = 0 + -5 3p = 0 + -5 Combine like terms: 0 + -5 = -5 3p = -5 Divide each side by '3'. p = -1.666666667 Simplifying p = -1.666666667Subproblem 2
Set the factor '(5 + 3p)' equal to zero and attempt to solve: Simplifying 5 + 3p = 0 Solving 5 + 3p = 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 + 3p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3p = 0 + -5 3p = 0 + -5 Combine like terms: 0 + -5 = -5 3p = -5 Divide each side by '3'. p = -1.666666667 Simplifying p = -1.666666667Solution
p = {-1.666666667, -1.666666667}
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