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Simplifying (2p + -3)(4p + 7) = 0 Reorder the terms: (-3 + 2p)(4p + 7) = 0 Reorder the terms: (-3 + 2p)(7 + 4p) = 0 Multiply (-3 + 2p) * (7 + 4p) (-3(7 + 4p) + 2p * (7 + 4p)) = 0 ((7 * -3 + 4p * -3) + 2p * (7 + 4p)) = 0 ((-21 + -12p) + 2p * (7 + 4p)) = 0 (-21 + -12p + (7 * 2p + 4p * 2p)) = 0 (-21 + -12p + (14p + 8p2)) = 0 Combine like terms: -12p + 14p = 2p (-21 + 2p + 8p2) = 0 Solving -21 + 2p + 8p2 = 0 Solving for variable 'p'. Factor a trinomial. (-7 + -4p)(3 + -2p) = 0Subproblem 1
Set the factor '(-7 + -4p)' equal to zero and attempt to solve: Simplifying -7 + -4p = 0 Solving -7 + -4p = 0 Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -4p = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4p = 0 + 7 -4p = 0 + 7 Combine like terms: 0 + 7 = 7 -4p = 7 Divide each side by '-4'. p = -1.75 Simplifying p = -1.75Subproblem 2
Set the factor '(3 + -2p)' equal to zero and attempt to solve: Simplifying 3 + -2p = 0 Solving 3 + -2p = 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 + -2p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2p = 0 + -3 -2p = 0 + -3 Combine like terms: 0 + -3 = -3 -2p = -3 Divide each side by '-2'. p = 1.5 Simplifying p = 1.5Solution
p = {-1.75, 1.5}
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