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Simplifying 32p = 3p2 + 20 Reorder the terms: 32p = 20 + 3p2 Solving 32p = 20 + 3p2 Solving for variable 'p'. Reorder the terms: -20 + 32p + -3p2 = 20 + 3p2 + -20 + -3p2 Reorder the terms: -20 + 32p + -3p2 = 20 + -20 + 3p2 + -3p2 Combine like terms: 20 + -20 = 0 -20 + 32p + -3p2 = 0 + 3p2 + -3p2 -20 + 32p + -3p2 = 3p2 + -3p2 Combine like terms: 3p2 + -3p2 = 0 -20 + 32p + -3p2 = 0 Factor a trinomial. (-10 + p)(2 + -3p) = 0Subproblem 1
Set the factor '(-10 + p)' equal to zero and attempt to solve: Simplifying -10 + p = 0 Solving -10 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + p = 0 + 10 Combine like terms: -10 + 10 = 0 0 + p = 0 + 10 p = 0 + 10 Combine like terms: 0 + 10 = 10 p = 10 Simplifying p = 10Subproblem 2
Set the factor '(2 + -3p)' equal to zero and attempt to solve: Simplifying 2 + -3p = 0 Solving 2 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3p = 0 + -2 -3p = 0 + -2 Combine like terms: 0 + -2 = -2 -3p = -2 Divide each side by '-3'. p = 0.6666666667 Simplifying p = 0.6666666667Solution
p = {10, 0.6666666667}
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