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Simplifying 0 = 27q + -1q2 + -1yq + -1(3) * q Multiply -1 * 3 0 = 27q + -1q2 + -1qy + -3q Reorder the terms: 0 = 27q + -3q + -1qy + -1q2 Combine like terms: 27q + -3q = 24q 0 = 24q + -1qy + -1q2 Solving 0 = 24q + -1qy + -1q2 Solving for variable 'q'. Remove the zero: -24q + qy + q2 = 24q + -1qy + -1q2 + -24q + qy + q2 Reorder the terms: -24q + qy + q2 = 24q + -24q + -1qy + qy + -1q2 + q2 Combine like terms: 24q + -24q = 0 -24q + qy + q2 = 0 + -1qy + qy + -1q2 + q2 -24q + qy + q2 = -1qy + qy + -1q2 + q2 Combine like terms: -1qy + qy = 0 -24q + qy + q2 = 0 + -1q2 + q2 -24q + qy + q2 = -1q2 + q2 Combine like terms: -1q2 + q2 = 0 -24q + qy + q2 = 0 Factor out the Greatest Common Factor (GCF), 'q'. q(-24 + y + q) = 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 '(-24 + y + q)' equal to zero and attempt to solve: Simplifying -24 + y + q = 0 Reorder the terms: -24 + q + y = 0 Solving -24 + q + y = 0 Move all terms containing q to the left, all other terms to the right. Add '24' to each side of the equation. -24 + q + 24 + y = 0 + 24 Reorder the terms: -24 + 24 + q + y = 0 + 24 Combine like terms: -24 + 24 = 0 0 + q + y = 0 + 24 q + y = 0 + 24 Combine like terms: 0 + 24 = 24 q + y = 24 Add '-1y' to each side of the equation. q + y + -1y = 24 + -1y Combine like terms: y + -1y = 0 q + 0 = 24 + -1y q = 24 + -1y Simplifying q = 24 + -1ySolution
q = {0, 24 + -1y}
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