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Simplifying 45q3 + -20q = 0 Reorder the terms: -20q + 45q3 = 0 Solving -20q + 45q3 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '5q'. 5q(-4 + 9q2) = 0 Factor a difference between two squares. 5q((2 + 3q)(-2 + 3q)) = 0 Ignore the factor 5.Subproblem 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 '(2 + 3q)' equal to zero and attempt to solve: Simplifying 2 + 3q = 0 Solving 2 + 3q = 0 Move all terms containing q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3q = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3q = 0 + -2 3q = 0 + -2 Combine like terms: 0 + -2 = -2 3q = -2 Divide each side by '3'. q = -0.6666666667 Simplifying q = -0.6666666667Subproblem 3
Set the factor '(-2 + 3q)' equal to zero and attempt to solve: Simplifying -2 + 3q = 0 Solving -2 + 3q = 0 Move all terms containing q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 3q = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3q = 0 + 2 3q = 0 + 2 Combine like terms: 0 + 2 = 2 3q = 2 Divide each side by '3'. q = 0.6666666667 Simplifying q = 0.6666666667Solution
q = {0, -0.6666666667, 0.6666666667}
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