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Simplifying 5p(2p + -3)(p + 7) = 0 Reorder the terms: 5p(-3 + 2p)(p + 7) = 0 Reorder the terms: 5p(-3 + 2p)(7 + p) = 0 Multiply (-3 + 2p) * (7 + p) 5p(-3(7 + p) + 2p * (7 + p)) = 0 5p((7 * -3 + p * -3) + 2p * (7 + p)) = 0 5p((-21 + -3p) + 2p * (7 + p)) = 0 5p(-21 + -3p + (7 * 2p + p * 2p)) = 0 5p(-21 + -3p + (14p + 2p2)) = 0 Combine like terms: -3p + 14p = 11p 5p(-21 + 11p + 2p2) = 0 (-21 * 5p + 11p * 5p + 2p2 * 5p) = 0 (-105p + 55p2 + 10p3) = 0 Solving -105p + 55p2 + 10p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '5p'. 5p(-21 + 11p + 2p2) = 0 Factor a trinomial. 5p((-7 + -1p)(3 + -2p)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0Subproblem 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 = -7Subproblem 3
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 = {0, -7, 1.5}
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