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Simplifying 4q2 + 7q + -3 = 3q + -3 Reorder the terms: -3 + 7q + 4q2 = 3q + -3 Reorder the terms: -3 + 7q + 4q2 = -3 + 3q Add '3' to each side of the equation. -3 + 7q + 3 + 4q2 = -3 + 3 + 3q Reorder the terms: -3 + 3 + 7q + 4q2 = -3 + 3 + 3q Combine like terms: -3 + 3 = 0 0 + 7q + 4q2 = -3 + 3 + 3q 7q + 4q2 = -3 + 3 + 3q Combine like terms: -3 + 3 = 0 7q + 4q2 = 0 + 3q 7q + 4q2 = 3q Solving 7q + 4q2 = 3q Solving for variable 'q'. Reorder the terms: 7q + -3q + 4q2 = 3q + -3q Combine like terms: 7q + -3q = 4q 4q + 4q2 = 3q + -3q Combine like terms: 3q + -3q = 0 4q + 4q2 = 0 Factor out the Greatest Common Factor (GCF), '4q'. 4q(1 + q) = 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 + q)' equal to zero and attempt to solve: Simplifying 1 + q = 0 Solving 1 + q = 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 + q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + q = 0 + -1 q = 0 + -1 Combine like terms: 0 + -1 = -1 q = -1 Simplifying q = -1Solution
q = {0, -1}
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