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Simplifying C(q) = 3q + 2q2 Multiply C * q qC = 3q + 2q2 Solving qC = 3q + 2q2 Solving for variable 'q'. Reorder the terms: -3q + qC + -2q2 = 3q + 2q2 + -3q + -2q2 Reorder the terms: -3q + qC + -2q2 = 3q + -3q + 2q2 + -2q2 Combine like terms: 3q + -3q = 0 -3q + qC + -2q2 = 0 + 2q2 + -2q2 -3q + qC + -2q2 = 2q2 + -2q2 Combine like terms: 2q2 + -2q2 = 0 -3q + qC + -2q2 = 0 Factor out the Greatest Common Factor (GCF), 'q'. q(-3 + C + -2q) = 0Subproblem 1
Set the factor 'q' equal to zero and attempt to solve: Simplifying q = 0 Solving q = 0 Move all terms containing q to the left, all other terms to the right. Simplifying q = 0Subproblem 2
Set the factor '(-3 + C + -2q)' equal to zero and attempt to solve: Simplifying -3 + C + -2q = 0 Solving -3 + C + -2q = 0 Move all terms containing q to the left, all other terms to the right. Add '3' to each side of the equation. -3 + C + 3 + -2q = 0 + 3 Reorder the terms: -3 + 3 + C + -2q = 0 + 3 Combine like terms: -3 + 3 = 0 0 + C + -2q = 0 + 3 C + -2q = 0 + 3 Combine like terms: 0 + 3 = 3 C + -2q = 3 Add '-1C' to each side of the equation. C + -1C + -2q = 3 + -1C Combine like terms: C + -1C = 0 0 + -2q = 3 + -1C -2q = 3 + -1C Divide each side by '-2'. q = -1.5 + 0.5C Simplifying q = -1.5 + 0.5CSolution
q = {0, -1.5 + 0.5C}
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