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Simplifying 2(3p + -4)(p + -3) = 0 Reorder the terms: 2(-4 + 3p)(p + -3) = 0 Reorder the terms: 2(-4 + 3p)(-3 + p) = 0 Multiply (-4 + 3p) * (-3 + p) 2(-4(-3 + p) + 3p * (-3 + p)) = 0 2((-3 * -4 + p * -4) + 3p * (-3 + p)) = 0 2((12 + -4p) + 3p * (-3 + p)) = 0 2(12 + -4p + (-3 * 3p + p * 3p)) = 0 2(12 + -4p + (-9p + 3p2)) = 0 Combine like terms: -4p + -9p = -13p 2(12 + -13p + 3p2) = 0 (12 * 2 + -13p * 2 + 3p2 * 2) = 0 (24 + -26p + 6p2) = 0 Solving 24 + -26p + 6p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -13p + 3p2) = 0 Factor a trinomial. 2((4 + -3p)(3 + -1p)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -3p)' equal to zero and attempt to solve: Simplifying 4 + -3p = 0 Solving 4 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3p = 0 + -4 -3p = 0 + -4 Combine like terms: 0 + -4 = -4 -3p = -4 Divide each side by '-3'. p = 1.333333333 Simplifying p = 1.333333333Subproblem 2
Set the factor '(3 + -1p)' equal to zero and attempt to solve: Simplifying 3 + -1p = 0 Solving 3 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1p = 0 + -3 -1p = 0 + -3 Combine like terms: 0 + -3 = -3 -1p = -3 Divide each side by '-1'. p = 3 Simplifying p = 3Solution
p = {1.333333333, 3}
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