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Simplifying 75v2 + 90vt + 27t2 = 0 Reorder the terms: 90tv + 27t2 + 75v2 = 0 Solving 90tv + 27t2 + 75v2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(30tv + 9t2 + 25v2) = 0 Factor a trinomial. 3((3t + 5v)(3t + 5v)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3t + 5v)' equal to zero and attempt to solve: Simplifying 3t + 5v = 0 Solving 3t + 5v = 0 Move all terms containing t to the left, all other terms to the right. Add '-5v' to each side of the equation. 3t + 5v + -5v = 0 + -5v Combine like terms: 5v + -5v = 0 3t + 0 = 0 + -5v 3t = 0 + -5v Remove the zero: 3t = -5v Divide each side by '3'. t = -1.666666667v Simplifying t = -1.666666667vSubproblem 2
Set the factor '(3t + 5v)' equal to zero and attempt to solve: Simplifying 3t + 5v = 0 Solving 3t + 5v = 0 Move all terms containing t to the left, all other terms to the right. Add '-5v' to each side of the equation. 3t + 5v + -5v = 0 + -5v Combine like terms: 5v + -5v = 0 3t + 0 = 0 + -5v 3t = 0 + -5v Remove the zero: 3t = -5v Divide each side by '3'. t = -1.666666667v Simplifying t = -1.666666667vSolution
t = {-1.666666667v, -1.666666667v}
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