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Simplifying (3p + 1)(p + -2) = 0 Reorder the terms: (1 + 3p)(p + -2) = 0 Reorder the terms: (1 + 3p)(-2 + p) = 0 Multiply (1 + 3p) * (-2 + p) (1(-2 + p) + 3p * (-2 + p)) = 0 ((-2 * 1 + p * 1) + 3p * (-2 + p)) = 0 ((-2 + 1p) + 3p * (-2 + p)) = 0 (-2 + 1p + (-2 * 3p + p * 3p)) = 0 (-2 + 1p + (-6p + 3p2)) = 0 Combine like terms: 1p + -6p = -5p (-2 + -5p + 3p2) = 0 Solving -2 + -5p + 3p2 = 0 Solving for variable 'p'. Factor a trinomial. (-1 + -3p)(2 + -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 '(2 + -1p)' equal to zero and attempt to solve: Simplifying 2 + -1p = 0 Solving 2 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1p = 0 + -2 -1p = 0 + -2 Combine like terms: 0 + -2 = -2 -1p = -2 Divide each side by '-1'. p = 2 Simplifying p = 2Solution
p = {-0.3333333333, 2}
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