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Simplifying 12q2 + -11qw + -15w2 = 0 Reorder the terms: -11qw + 12q2 + -15w2 = 0 Solving -11qw + 12q2 + -15w2 = 0 Solving for variable 'q'. Factor a trinomial. (3q + -5w)(4q + 3w) = 0Subproblem 1
Set the factor '(3q + -5w)' equal to zero and attempt to solve: Simplifying 3q + -5w = 0 Solving 3q + -5w = 0 Move all terms containing q to the left, all other terms to the right. Add '5w' to each side of the equation. 3q + -5w + 5w = 0 + 5w Combine like terms: -5w + 5w = 0 3q + 0 = 0 + 5w 3q = 0 + 5w Remove the zero: 3q = 5w Divide each side by '3'. q = 1.666666667w Simplifying q = 1.666666667wSubproblem 2
Set the factor '(4q + 3w)' equal to zero and attempt to solve: Simplifying 4q + 3w = 0 Solving 4q + 3w = 0 Move all terms containing q to the left, all other terms to the right. Add '-3w' to each side of the equation. 4q + 3w + -3w = 0 + -3w Combine like terms: 3w + -3w = 0 4q + 0 = 0 + -3w 4q = 0 + -3w Remove the zero: 4q = -3w Divide each side by '4'. q = -0.75w Simplifying q = -0.75wSolution
q = {1.666666667w, -0.75w}
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