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Simplifying 15p2 = p + 6 Reorder the terms: 15p2 = 6 + p Solving 15p2 = 6 + p Solving for variable 'p'. Reorder the terms: -6 + -1p + 15p2 = 6 + p + -6 + -1p Reorder the terms: -6 + -1p + 15p2 = 6 + -6 + p + -1p Combine like terms: 6 + -6 = 0 -6 + -1p + 15p2 = 0 + p + -1p -6 + -1p + 15p2 = p + -1p Combine like terms: p + -1p = 0 -6 + -1p + 15p2 = 0 Factor a trinomial. (-3 + -5p)(2 + -3p) = 0Subproblem 1
Set the factor '(-3 + -5p)' equal to zero and attempt to solve: Simplifying -3 + -5p = 0 Solving -3 + -5p = 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 + -5p = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5p = 0 + 3 -5p = 0 + 3 Combine like terms: 0 + 3 = 3 -5p = 3 Divide each side by '-5'. p = -0.6 Simplifying p = -0.6Subproblem 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 = {-0.6, 0.6666666667}
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