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Simplifying (5q + 11)(2q + -3) = 0 Reorder the terms: (11 + 5q)(2q + -3) = 0 Reorder the terms: (11 + 5q)(-3 + 2q) = 0 Multiply (11 + 5q) * (-3 + 2q) (11(-3 + 2q) + 5q * (-3 + 2q)) = 0 ((-3 * 11 + 2q * 11) + 5q * (-3 + 2q)) = 0 ((-33 + 22q) + 5q * (-3 + 2q)) = 0 (-33 + 22q + (-3 * 5q + 2q * 5q)) = 0 (-33 + 22q + (-15q + 10q2)) = 0 Combine like terms: 22q + -15q = 7q (-33 + 7q + 10q2) = 0 Solving -33 + 7q + 10q2 = 0 Solving for variable 'q'. Factor a trinomial. (-11 + -5q)(3 + -2q) = 0Subproblem 1
Set the factor '(-11 + -5q)' equal to zero and attempt to solve: Simplifying -11 + -5q = 0 Solving -11 + -5q = 0 Move all terms containing q to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -5q = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -5q = 0 + 11 -5q = 0 + 11 Combine like terms: 0 + 11 = 11 -5q = 11 Divide each side by '-5'. q = -2.2 Simplifying q = -2.2Subproblem 2
Set the factor '(3 + -2q)' equal to zero and attempt to solve: Simplifying 3 + -2q = 0 Solving 3 + -2q = 0 Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2q = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2q = 0 + -3 -2q = 0 + -3 Combine like terms: 0 + -3 = -3 -2q = -3 Divide each side by '-2'. q = 1.5 Simplifying q = 1.5Solution
q = {-2.2, 1.5}
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