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Simplifying (2p + 3)(p + -7) = 0 Reorder the terms: (3 + 2p)(p + -7) = 0 Reorder the terms: (3 + 2p)(-7 + p) = 0 Multiply (3 + 2p) * (-7 + p) (3(-7 + p) + 2p * (-7 + p)) = 0 ((-7 * 3 + p * 3) + 2p * (-7 + p)) = 0 ((-21 + 3p) + 2p * (-7 + p)) = 0 (-21 + 3p + (-7 * 2p + p * 2p)) = 0 (-21 + 3p + (-14p + 2p2)) = 0 Combine like terms: 3p + -14p = -11p (-21 + -11p + 2p2) = 0 Solving -21 + -11p + 2p2 = 0 Solving for variable 'p'. Factor a trinomial. (-3 + -2p)(7 + -1p) = 0Subproblem 1
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 = -1.5Subproblem 2
Set the factor '(7 + -1p)' equal to zero and attempt to solve: Simplifying 7 + -1p = 0 Solving 7 + -1p = 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 + -1p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1p = 0 + -7 -1p = 0 + -7 Combine like terms: 0 + -7 = -7 -1p = -7 Divide each side by '-1'. p = 7 Simplifying p = 7Solution
p = {-1.5, 7}
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