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Simplifying (2p + -4)(3p + 1) = 0 Reorder the terms: (-4 + 2p)(3p + 1) = 0 Reorder the terms: (-4 + 2p)(1 + 3p) = 0 Multiply (-4 + 2p) * (1 + 3p) (-4(1 + 3p) + 2p * (1 + 3p)) = 0 ((1 * -4 + 3p * -4) + 2p * (1 + 3p)) = 0 ((-4 + -12p) + 2p * (1 + 3p)) = 0 (-4 + -12p + (1 * 2p + 3p * 2p)) = 0 (-4 + -12p + (2p + 6p2)) = 0 Combine like terms: -12p + 2p = -10p (-4 + -10p + 6p2) = 0 Solving -4 + -10p + 6p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -5p + 3p2) = 0 Factor a trinomial. 2((-1 + -3p)(2 + -1p)) = 0 Ignore the factor 2.Subproblem 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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