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Simplifying 12w2 + 36wt + 27t2 = 0 Reorder the terms: 36tw + 27t2 + 12w2 = 0 Solving 36tw + 27t2 + 12w2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(12tw + 9t2 + 4w2) = 0 Factor a trinomial. 3((3t + 2w)(3t + 2w)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3t + 2w)' equal to zero and attempt to solve: Simplifying 3t + 2w = 0 Solving 3t + 2w = 0 Move all terms containing t to the left, all other terms to the right. Add '-2w' to each side of the equation. 3t + 2w + -2w = 0 + -2w Combine like terms: 2w + -2w = 0 3t + 0 = 0 + -2w 3t = 0 + -2w Remove the zero: 3t = -2w Divide each side by '3'. t = -0.6666666667w Simplifying t = -0.6666666667wSubproblem 2
Set the factor '(3t + 2w)' equal to zero and attempt to solve: Simplifying 3t + 2w = 0 Solving 3t + 2w = 0 Move all terms containing t to the left, all other terms to the right. Add '-2w' to each side of the equation. 3t + 2w + -2w = 0 + -2w Combine like terms: 2w + -2w = 0 3t + 0 = 0 + -2w 3t = 0 + -2w Remove the zero: 3t = -2w Divide each side by '3'. t = -0.6666666667w Simplifying t = -0.6666666667wSolution
t = {-0.6666666667w, -0.6666666667w}
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