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Simplifying (4p + -1)(16p2 + -1 + 4p + 1) = 0 Reorder the terms: (-1 + 4p)(16p2 + -1 + 4p + 1) = 0 Reorder the terms: (-1 + 4p)(-1 + 1 + 4p + 16p2) = 0 Combine like terms: -1 + 1 = 0 (-1 + 4p)(0 + 4p + 16p2) = 0 (-1 + 4p)(4p + 16p2) = 0 Multiply (-1 + 4p) * (4p + 16p2) (-1(4p + 16p2) + 4p * (4p + 16p2)) = 0 ((4p * -1 + 16p2 * -1) + 4p * (4p + 16p2)) = 0 ((-4p + -16p2) + 4p * (4p + 16p2)) = 0 (-4p + -16p2 + (4p * 4p + 16p2 * 4p)) = 0 (-4p + -16p2 + (16p2 + 64p3)) = 0 Combine like terms: -16p2 + 16p2 = 0 (-4p + 0 + 64p3) = 0 (-4p + 64p3) = 0 Solving -4p + 64p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '4p'. 4p(-1 + 16p2) = 0 Factor a difference between two squares. 4p((1 + 4p)(-1 + 4p)) = 0 Ignore the factor 4.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 + 4p)' equal to zero and attempt to solve: Simplifying 1 + 4p = 0 Solving 1 + 4p = 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 + 4p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4p = 0 + -1 4p = 0 + -1 Combine like terms: 0 + -1 = -1 4p = -1 Divide each side by '4'. p = -0.25 Simplifying p = -0.25Subproblem 3
Set the factor '(-1 + 4p)' equal to zero and attempt to solve: Simplifying -1 + 4p = 0 Solving -1 + 4p = 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 + 4p = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4p = 0 + 1 4p = 0 + 1 Combine like terms: 0 + 1 = 1 4p = 1 Divide each side by '4'. p = 0.25 Simplifying p = 0.25Solution
p = {0, -0.25, 0.25}
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