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Simplifying (6p + -1)(4p + 7) = 0 Reorder the terms: (-1 + 6p)(4p + 7) = 0 Reorder the terms: (-1 + 6p)(7 + 4p) = 0 Multiply (-1 + 6p) * (7 + 4p) (-1(7 + 4p) + 6p * (7 + 4p)) = 0 ((7 * -1 + 4p * -1) + 6p * (7 + 4p)) = 0 ((-7 + -4p) + 6p * (7 + 4p)) = 0 (-7 + -4p + (7 * 6p + 4p * 6p)) = 0 (-7 + -4p + (42p + 24p2)) = 0 Combine like terms: -4p + 42p = 38p (-7 + 38p + 24p2) = 0 Solving -7 + 38p + 24p2 = 0 Solving for variable 'p'. Factor a trinomial. (-7 + -4p)(1 + -6p) = 0Subproblem 1
Set the factor '(-7 + -4p)' equal to zero and attempt to solve: Simplifying -7 + -4p = 0 Solving -7 + -4p = 0 Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -4p = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4p = 0 + 7 -4p = 0 + 7 Combine like terms: 0 + 7 = 7 -4p = 7 Divide each side by '-4'. p = -1.75 Simplifying p = -1.75Subproblem 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 = {-1.75, 0.1666666667}
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