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Simplifying (p + 8)(6p + -1) = 0 Reorder the terms: (8 + p)(6p + -1) = 0 Reorder the terms: (8 + p)(-1 + 6p) = 0 Multiply (8 + p) * (-1 + 6p) (8(-1 + 6p) + p(-1 + 6p)) = 0 ((-1 * 8 + 6p * 8) + p(-1 + 6p)) = 0 ((-8 + 48p) + p(-1 + 6p)) = 0 (-8 + 48p + (-1 * p + 6p * p)) = 0 (-8 + 48p + (-1p + 6p2)) = 0 Combine like terms: 48p + -1p = 47p (-8 + 47p + 6p2) = 0 Solving -8 + 47p + 6p2 = 0 Solving for variable 'p'. Factor a trinomial. (-8 + -1p)(1 + -6p) = 0Subproblem 1
Set the factor '(-8 + -1p)' equal to zero and attempt to solve: Simplifying -8 + -1p = 0 Solving -8 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1p = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1p = 0 + 8 -1p = 0 + 8 Combine like terms: 0 + 8 = 8 -1p = 8 Divide each side by '-1'. p = -8 Simplifying p = -8Subproblem 2
Set the factor '(1 + -6p)' equal to zero and attempt to solve: Simplifying 1 + -6p = 0 Solving 1 + -6p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -6p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6p = 0 + -1 -6p = 0 + -1 Combine like terms: 0 + -1 = -1 -6p = -1 Divide each side by '-6'. p = 0.1666666667 Simplifying p = 0.1666666667Solution
p = {-8, 0.1666666667}
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