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Simplifying p(4p + 5)(4p + -5) = 0 Reorder the terms: p(5 + 4p)(4p + -5) = 0 Reorder the terms: p(5 + 4p)(-5 + 4p) = 0 Multiply (5 + 4p) * (-5 + 4p) p(5(-5 + 4p) + 4p * (-5 + 4p)) = 0 p((-5 * 5 + 4p * 5) + 4p * (-5 + 4p)) = 0 p((-25 + 20p) + 4p * (-5 + 4p)) = 0 p(-25 + 20p + (-5 * 4p + 4p * 4p)) = 0 p(-25 + 20p + (-20p + 16p2)) = 0 Combine like terms: 20p + -20p = 0 p(-25 + 0 + 16p2) = 0 p(-25 + 16p2) = 0 (-25 * p + 16p2 * p) = 0 (-25p + 16p3) = 0 Solving -25p + 16p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(-25 + 16p2) = 0 Factor a difference between two squares. p((5 + 4p)(-5 + 4p)) = 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 '(5 + 4p)' equal to zero and attempt to solve: Simplifying 5 + 4p = 0 Solving 5 + 4p = 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 + 4p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4p = 0 + -5 4p = 0 + -5 Combine like terms: 0 + -5 = -5 4p = -5 Divide each side by '4'. p = -1.25 Simplifying p = -1.25Subproblem 3
Set the factor '(-5 + 4p)' equal to zero and attempt to solve: Simplifying -5 + 4p = 0 Solving -5 + 4p = 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 + 4p = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4p = 0 + 5 4p = 0 + 5 Combine like terms: 0 + 5 = 5 4p = 5 Divide each side by '4'. p = 1.25 Simplifying p = 1.25Solution
p = {0, -1.25, 1.25}
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