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