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Simplifying p(7p + 3)(7p + -3) = 0 Reorder the terms: p(3 + 7p)(7p + -3) = 0 Reorder the terms: p(3 + 7p)(-3 + 7p) = 0 Multiply (3 + 7p) * (-3 + 7p) p(3(-3 + 7p) + 7p * (-3 + 7p)) = 0 p((-3 * 3 + 7p * 3) + 7p * (-3 + 7p)) = 0 p((-9 + 21p) + 7p * (-3 + 7p)) = 0 p(-9 + 21p + (-3 * 7p + 7p * 7p)) = 0 p(-9 + 21p + (-21p + 49p2)) = 0 Combine like terms: 21p + -21p = 0 p(-9 + 0 + 49p2) = 0 p(-9 + 49p2) = 0 (-9 * p + 49p2 * p) = 0 (-9p + 49p3) = 0 Solving -9p + 49p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(-9 + 49p2) = 0 Factor a difference between two squares. p((3 + 7p)(-3 + 7p)) = 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 + 7p)' equal to zero and attempt to solve: Simplifying 3 + 7p = 0 Solving 3 + 7p = 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 + 7p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7p = 0 + -3 7p = 0 + -3 Combine like terms: 0 + -3 = -3 7p = -3 Divide each side by '7'. p = -0.4285714286 Simplifying p = -0.4285714286Subproblem 3
Set the factor '(-3 + 7p)' equal to zero and attempt to solve: Simplifying -3 + 7p = 0 Solving -3 + 7p = 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 + 7p = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 7p = 0 + 3 7p = 0 + 3 Combine like terms: 0 + 3 = 3 7p = 3 Divide each side by '7'. p = 0.4285714286 Simplifying p = 0.4285714286Solution
p = {0, -0.4285714286, 0.4285714286}
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