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Simplifying 45p3 + -20p = 0 Reorder the terms: -20p + 45p3 = 0 Solving -20p + 45p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '5p'. 5p(-4 + 9p2) = 0 Factor a difference between two squares. 5p((2 + 3p)(-2 + 3p)) = 0 Ignore the factor 5.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 '(2 + 3p)' equal to zero and attempt to solve: Simplifying 2 + 3p = 0 Solving 2 + 3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3p = 0 + -2 3p = 0 + -2 Combine like terms: 0 + -2 = -2 3p = -2 Divide each side by '3'. p = -0.6666666667 Simplifying p = -0.6666666667Subproblem 3
Set the factor '(-2 + 3p)' equal to zero and attempt to solve: Simplifying -2 + 3p = 0 Solving -2 + 3p = 0 Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 3p = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3p = 0 + 2 3p = 0 + 2 Combine like terms: 0 + 2 = 2 3p = 2 Divide each side by '3'. p = 0.6666666667 Simplifying p = 0.6666666667Solution
p = {0, -0.6666666667, 0.6666666667}
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