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Simplifying (4p + -4)(4p + -3) = 0 Reorder the terms: (-4 + 4p)(4p + -3) = 0 Reorder the terms: (-4 + 4p)(-3 + 4p) = 0 Multiply (-4 + 4p) * (-3 + 4p) (-4(-3 + 4p) + 4p * (-3 + 4p)) = 0 ((-3 * -4 + 4p * -4) + 4p * (-3 + 4p)) = 0 ((12 + -16p) + 4p * (-3 + 4p)) = 0 (12 + -16p + (-3 * 4p + 4p * 4p)) = 0 (12 + -16p + (-12p + 16p2)) = 0 Combine like terms: -16p + -12p = -28p (12 + -28p + 16p2) = 0 Solving 12 + -28p + 16p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -7p + 4p2) = 0 Factor a trinomial. 4((3 + -4p)(1 + -1p)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -4p)' equal to zero and attempt to solve: Simplifying 3 + -4p = 0 Solving 3 + -4p = 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 + -4p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4p = 0 + -3 -4p = 0 + -3 Combine like terms: 0 + -3 = -3 -4p = -3 Divide each side by '-4'. p = 0.75 Simplifying p = 0.75Subproblem 2
Set the factor '(1 + -1p)' equal to zero and attempt to solve: Simplifying 1 + -1p = 0 Solving 1 + -1p = 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 + -1p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1p = 0 + -1 -1p = 0 + -1 Combine like terms: 0 + -1 = -1 -1p = -1 Divide each side by '-1'. p = 1 Simplifying p = 1Solution
p = {0.75, 1}
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