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Simplifying 4q(-4q + -4q2 + -1) = 0 Reorder the terms: 4q(-1 + -4q + -4q2) = 0 (-1 * 4q + -4q * 4q + -4q2 * 4q) = 0 (-4q + -16q2 + -16q3) = 0 Solving -4q + -16q2 + -16q3 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '-4q'. -4q(1 + 4q + 4q2) = 0 Factor a trinomial. -4q((1 + 2q)(1 + 2q)) = 0 Ignore the factor -4.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 '(1 + 2q)' equal to zero and attempt to solve: Simplifying 1 + 2q = 0 Solving 1 + 2q = 0 Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2q = 0 + -1 2q = 0 + -1 Combine like terms: 0 + -1 = -1 2q = -1 Divide each side by '2'. q = -0.5 Simplifying q = -0.5Subproblem 3
Set the factor '(1 + 2q)' equal to zero and attempt to solve: Simplifying 1 + 2q = 0 Solving 1 + 2q = 0 Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2q = 0 + -1 2q = 0 + -1 Combine like terms: 0 + -1 = -1 2q = -1 Divide each side by '2'. q = -0.5 Simplifying q = -0.5Solution
q = {0, -0.5, -0.5}
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