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Simplifying (q + -1)(6q + -7) = 0 Reorder the terms: (-1 + q)(6q + -7) = 0 Reorder the terms: (-1 + q)(-7 + 6q) = 0 Multiply (-1 + q) * (-7 + 6q) (-1(-7 + 6q) + q(-7 + 6q)) = 0 ((-7 * -1 + 6q * -1) + q(-7 + 6q)) = 0 ((7 + -6q) + q(-7 + 6q)) = 0 (7 + -6q + (-7 * q + 6q * q)) = 0 (7 + -6q + (-7q + 6q2)) = 0 Combine like terms: -6q + -7q = -13q (7 + -13q + 6q2) = 0 Solving 7 + -13q + 6q2 = 0 Solving for variable 'q'. Factor a trinomial. (1 + -1q)(7 + -6q) = 0Subproblem 1
Set the factor '(1 + -1q)' equal to zero and attempt to solve: Simplifying 1 + -1q = 0 Solving 1 + -1q = 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 + -1q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1q = 0 + -1 -1q = 0 + -1 Combine like terms: 0 + -1 = -1 -1q = -1 Divide each side by '-1'. q = 1 Simplifying q = 1Subproblem 2
Set the factor '(7 + -6q)' equal to zero and attempt to solve: Simplifying 7 + -6q = 0 Solving 7 + -6q = 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 + -6q = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6q = 0 + -7 -6q = 0 + -7 Combine like terms: 0 + -7 = -7 -6q = -7 Divide each side by '-6'. q = 1.166666667 Simplifying q = 1.166666667Solution
q = {1, 1.166666667}
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