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Simplifying (q + 2)(q + -5) = 0 Reorder the terms: (2 + q)(q + -5) = 0 Reorder the terms: (2 + q)(-5 + q) = 0 Multiply (2 + q) * (-5 + q) (2(-5 + q) + q(-5 + q)) = 0 ((-5 * 2 + q * 2) + q(-5 + q)) = 0 ((-10 + 2q) + q(-5 + q)) = 0 (-10 + 2q + (-5 * q + q * q)) = 0 (-10 + 2q + (-5q + q2)) = 0 Combine like terms: 2q + -5q = -3q (-10 + -3q + q2) = 0 Solving -10 + -3q + q2 = 0 Solving for variable 'q'. Factor a trinomial. (-2 + -1q)(5 + -1q) = 0Subproblem 1
Set the factor '(-2 + -1q)' equal to zero and attempt to solve: Simplifying -2 + -1q = 0 Solving -2 + -1q = 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 + -1q = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1q = 0 + 2 -1q = 0 + 2 Combine like terms: 0 + 2 = 2 -1q = 2 Divide each side by '-1'. q = -2 Simplifying q = -2Subproblem 2
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 = 5Solution
q = {-2, 5}
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