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Simplifying s(p) = 3p + -4p2 Multiply s * p ps = 3p + -4p2 Solving ps = 3p + -4p2 Solving for variable 'p'. Reorder the terms: -3p + ps + 4p2 = 3p + -4p2 + -3p + 4p2 Reorder the terms: -3p + ps + 4p2 = 3p + -3p + -4p2 + 4p2 Combine like terms: 3p + -3p = 0 -3p + ps + 4p2 = 0 + -4p2 + 4p2 -3p + ps + 4p2 = -4p2 + 4p2 Combine like terms: -4p2 + 4p2 = 0 -3p + ps + 4p2 = 0 Factor out the Greatest Common Factor (GCF), 'p'. p(-3 + s + 4p) = 0Subproblem 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 '(-3 + s + 4p)' equal to zero and attempt to solve: Simplifying -3 + s + 4p = 0 Reorder the terms: -3 + 4p + s = 0 Solving -3 + 4p + s = 0 Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 4p + 3 + s = 0 + 3 Reorder the terms: -3 + 3 + 4p + s = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4p + s = 0 + 3 4p + s = 0 + 3 Combine like terms: 0 + 3 = 3 4p + s = 3 Add '-1s' to each side of the equation. 4p + s + -1s = 3 + -1s Combine like terms: s + -1s = 0 4p + 0 = 3 + -1s 4p = 3 + -1s Divide each side by '4'. p = 0.75 + -0.25s Simplifying p = 0.75 + -0.25sSolution
p = {0, 0.75 + -0.25s}
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