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Simplifying 23p = 3p2 + 30 Reorder the terms: 23p = 30 + 3p2 Solving 23p = 30 + 3p2 Solving for variable 'p'. Reorder the terms: -30 + 23p + -3p2 = 30 + 3p2 + -30 + -3p2 Reorder the terms: -30 + 23p + -3p2 = 30 + -30 + 3p2 + -3p2 Combine like terms: 30 + -30 = 0 -30 + 23p + -3p2 = 0 + 3p2 + -3p2 -30 + 23p + -3p2 = 3p2 + -3p2 Combine like terms: 3p2 + -3p2 = 0 -30 + 23p + -3p2 = 0 Factor a trinomial. (-6 + p)(5 + -3p) = 0Subproblem 1
Set the factor '(-6 + p)' equal to zero and attempt to solve: Simplifying -6 + p = 0 Solving -6 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + p = 0 + 6 Combine like terms: -6 + 6 = 0 0 + p = 0 + 6 p = 0 + 6 Combine like terms: 0 + 6 = 6 p = 6 Simplifying p = 6Subproblem 2
Set the factor '(5 + -3p)' equal to zero and attempt to solve: Simplifying 5 + -3p = 0 Solving 5 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3p = 0 + -5 -3p = 0 + -5 Combine like terms: 0 + -5 = -5 -3p = -5 Divide each side by '-3'. p = 1.666666667 Simplifying p = 1.666666667Solution
p = {6, 1.666666667}
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