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Simplifying (q + -7)(q + -5) = 0 Reorder the terms: (-7 + q)(q + -5) = 0 Reorder the terms: (-7 + q)(-5 + q) = 0 Multiply (-7 + q) * (-5 + q) (-7(-5 + q) + q(-5 + q)) = 0 ((-5 * -7 + q * -7) + q(-5 + q)) = 0 ((35 + -7q) + q(-5 + q)) = 0 (35 + -7q + (-5 * q + q * q)) = 0 (35 + -7q + (-5q + q2)) = 0 Combine like terms: -7q + -5q = -12q (35 + -12q + q2) = 0 Solving 35 + -12q + q2 = 0 Solving for variable 'q'. Factor a trinomial. (5 + -1q)(7 + -1q) = 0Subproblem 1
Set the factor '(5 + -1q)' equal to zero and attempt to solve: Simplifying 5 + -1q = 0 Solving 5 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1q = 0 + -5 -1q = 0 + -5 Combine like terms: 0 + -5 = -5 -1q = -5 Divide each side by '-1'. q = 5 Simplifying q = 5Subproblem 2
Set the factor '(7 + -1q)' equal to zero and attempt to solve: Simplifying 7 + -1q = 0 Solving 7 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1q = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1q = 0 + -7 -1q = 0 + -7 Combine like terms: 0 + -7 = -7 -1q = -7 Divide each side by '-1'. q = 7 Simplifying q = 7Solution
q = {5, 7}
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