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Simplifying (4p + 3)(p + -4) = 0 Reorder the terms: (3 + 4p)(p + -4) = 0 Reorder the terms: (3 + 4p)(-4 + p) = 0 Multiply (3 + 4p) * (-4 + p) (3(-4 + p) + 4p * (-4 + p)) = 0 ((-4 * 3 + p * 3) + 4p * (-4 + p)) = 0 ((-12 + 3p) + 4p * (-4 + p)) = 0 (-12 + 3p + (-4 * 4p + p * 4p)) = 0 (-12 + 3p + (-16p + 4p2)) = 0 Combine like terms: 3p + -16p = -13p (-12 + -13p + 4p2) = 0 Solving -12 + -13p + 4p2 = 0 Solving for variable 'p'. Factor a trinomial. (-3 + -4p)(4 + -1p) = 0Subproblem 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 '(4 + -1p)' equal to zero and attempt to solve: Simplifying 4 + -1p = 0 Solving 4 + -1p = 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 + -1p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1p = 0 + -4 -1p = 0 + -4 Combine like terms: 0 + -4 = -4 -1p = -4 Divide each side by '-1'. p = 4 Simplifying p = 4Solution
p = {-0.75, 4}
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