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Simplifying (1 + -3p)(7 + -1p) = 0 Multiply (1 + -3p) * (7 + -1p) (1(7 + -1p) + -3p * (7 + -1p)) = 0 ((7 * 1 + -1p * 1) + -3p * (7 + -1p)) = 0 ((7 + -1p) + -3p * (7 + -1p)) = 0 (7 + -1p + (7 * -3p + -1p * -3p)) = 0 (7 + -1p + (-21p + 3p2)) = 0 Combine like terms: -1p + -21p = -22p (7 + -22p + 3p2) = 0 Solving 7 + -22p + 3p2 = 0 Solving for variable 'p'. Factor a trinomial. (1 + -3p)(7 + -1p) = 0Subproblem 1
Set the factor '(1 + -3p)' equal to zero and attempt to solve: Simplifying 1 + -3p = 0 Solving 1 + -3p = 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 + -3p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3p = 0 + -1 -3p = 0 + -1 Combine like terms: 0 + -1 = -1 -3p = -1 Divide each side by '-3'. p = 0.3333333333 Simplifying p = 0.3333333333Subproblem 2
Set the factor '(7 + -1p)' equal to zero and attempt to solve: Simplifying 7 + -1p = 0 Solving 7 + -1p = 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 + -1p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1p = 0 + -7 -1p = 0 + -7 Combine like terms: 0 + -7 = -7 -1p = -7 Divide each side by '-1'. p = 7 Simplifying p = 7Solution
p = {0.3333333333, 7}
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