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Simplifying 5q4 + -60q3 + 135q2 = 0 Reorder the terms: 135q2 + -60q3 + 5q4 = 0 Solving 135q2 + -60q3 + 5q4 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '5q2'. 5q2(27 + -12q + q2) = 0 Factor a trinomial. 5q2((3 + -1q)(9 + -1q)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'q2' equal to zero and attempt to solve: Simplifying q2 = 0 Solving q2 = 0 Move all terms containing q to the left, all other terms to the right. Simplifying q2 = 0 Take the square root of each side: q = {0}Subproblem 2
Set the factor '(3 + -1q)' equal to zero and attempt to solve: Simplifying 3 + -1q = 0 Solving 3 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1q = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1q = 0 + -3 -1q = 0 + -3 Combine like terms: 0 + -3 = -3 -1q = -3 Divide each side by '-1'. q = 3 Simplifying q = 3Subproblem 3
Set the factor '(9 + -1q)' equal to zero and attempt to solve: Simplifying 9 + -1q = 0 Solving 9 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1q = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1q = 0 + -9 -1q = 0 + -9 Combine like terms: 0 + -9 = -9 -1q = -9 Divide each side by '-1'. q = 9 Simplifying q = 9Solution
q = {0, 3, 9}
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