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Simplifying p(8p + 3)(8p + -3) = 0 Reorder the terms: p(3 + 8p)(8p + -3) = 0 Reorder the terms: p(3 + 8p)(-3 + 8p) = 0 Multiply (3 + 8p) * (-3 + 8p) p(3(-3 + 8p) + 8p * (-3 + 8p)) = 0 p((-3 * 3 + 8p * 3) + 8p * (-3 + 8p)) = 0 p((-9 + 24p) + 8p * (-3 + 8p)) = 0 p(-9 + 24p + (-3 * 8p + 8p * 8p)) = 0 p(-9 + 24p + (-24p + 64p2)) = 0 Combine like terms: 24p + -24p = 0 p(-9 + 0 + 64p2) = 0 p(-9 + 64p2) = 0 (-9 * p + 64p2 * p) = 0 (-9p + 64p3) = 0 Solving -9p + 64p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(-9 + 64p2) = 0 Factor a difference between two squares. p((3 + 8p)(-3 + 8p)) = 0Subproblem 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 '(3 + 8p)' equal to zero and attempt to solve: Simplifying 3 + 8p = 0 Solving 3 + 8p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 8p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8p = 0 + -3 8p = 0 + -3 Combine like terms: 0 + -3 = -3 8p = -3 Divide each side by '8'. p = -0.375 Simplifying p = -0.375Subproblem 3
Set the factor '(-3 + 8p)' equal to zero and attempt to solve: Simplifying -3 + 8p = 0 Solving -3 + 8p = 0 Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 8p = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 8p = 0 + 3 8p = 0 + 3 Combine like terms: 0 + 3 = 3 8p = 3 Divide each side by '8'. p = 0.375 Simplifying p = 0.375Solution
p = {0, -0.375, 0.375}
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