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Simplifying p(7p + 6)(7p + -6) = 0 Reorder the terms: p(6 + 7p)(7p + -6) = 0 Reorder the terms: p(6 + 7p)(-6 + 7p) = 0 Multiply (6 + 7p) * (-6 + 7p) p(6(-6 + 7p) + 7p * (-6 + 7p)) = 0 p((-6 * 6 + 7p * 6) + 7p * (-6 + 7p)) = 0 p((-36 + 42p) + 7p * (-6 + 7p)) = 0 p(-36 + 42p + (-6 * 7p + 7p * 7p)) = 0 p(-36 + 42p + (-42p + 49p2)) = 0 Combine like terms: 42p + -42p = 0 p(-36 + 0 + 49p2) = 0 p(-36 + 49p2) = 0 (-36 * p + 49p2 * p) = 0 (-36p + 49p3) = 0 Solving -36p + 49p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(-36 + 49p2) = 0 Factor a difference between two squares. p((6 + 7p)(-6 + 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 '(6 + 7p)' equal to zero and attempt to solve: Simplifying 6 + 7p = 0 Solving 6 + 7p = 0 Move all terms containing p to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 7p = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7p = 0 + -6 7p = 0 + -6 Combine like terms: 0 + -6 = -6 7p = -6 Divide each side by '7'. p = -0.8571428571 Simplifying p = -0.8571428571Subproblem 3
Set the factor '(-6 + 7p)' equal to zero and attempt to solve: Simplifying -6 + 7p = 0 Solving -6 + 7p = 0 Move all terms containing p to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + 7p = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 7p = 0 + 6 7p = 0 + 6 Combine like terms: 0 + 6 = 6 7p = 6 Divide each side by '7'. p = 0.8571428571 Simplifying p = 0.8571428571Solution
p = {0, -0.8571428571, 0.8571428571}
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