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Simplifying 8p5 = 400p3 + -392p Reorder the terms: 8p5 = -392p + 400p3 Solving 8p5 = -392p + 400p3 Solving for variable 'p'. Reorder the terms: 392p + -400p3 + 8p5 = -392p + 400p3 + 392p + -400p3 Reorder the terms: 392p + -400p3 + 8p5 = -392p + 392p + 400p3 + -400p3 Combine like terms: -392p + 392p = 0 392p + -400p3 + 8p5 = 0 + 400p3 + -400p3 392p + -400p3 + 8p5 = 400p3 + -400p3 Combine like terms: 400p3 + -400p3 = 0 392p + -400p3 + 8p5 = 0 Factor out the Greatest Common Factor (GCF), '8p'. 8p(49 + -50p2 + p4) = 0 Factor a trinomial. 8p((1 + -1p2)(49 + -1p2)) = 0 Factor a difference between two squares. 8p(((1 + p)(1 + -1p))(49 + -1p2)) = 0 Factor a difference between two squares. 8p(((7 + p)(7 + -1p))(1 + p)(1 + -1p)) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0Subproblem 2
Set the factor '(1 + p)' equal to zero and attempt to solve: Simplifying 1 + p = 0 Solving 1 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + p = 0 + -1 p = 0 + -1 Combine like terms: 0 + -1 = -1 p = -1 Simplifying p = -1Subproblem 3
Set the factor '(1 + -1p)' equal to zero and attempt to solve: Simplifying 1 + -1p = 0 Solving 1 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1p = 0 + -1 -1p = 0 + -1 Combine like terms: 0 + -1 = -1 -1p = -1 Divide each side by '-1'. p = 1 Simplifying p = 1Subproblem 4
Set the factor '(7 + p)' equal to zero and attempt to solve: Simplifying 7 + p = 0 Solving 7 + p = 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 + p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + p = 0 + -7 p = 0 + -7 Combine like terms: 0 + -7 = -7 p = -7 Simplifying p = -7Subproblem 5
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 = {0, -1, 1, -7, 7}
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