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Simplifying 18v2 + -27vt + 10t2 = 0 Reorder the terms: -27tv + 10t2 + 18v2 = 0 Solving -27tv + 10t2 + 18v2 = 0 Solving for variable 't'. Factor a trinomial. (2t + -3v)(5t + -6v) = 0Subproblem 1
Set the factor '(2t + -3v)' equal to zero and attempt to solve: Simplifying 2t + -3v = 0 Solving 2t + -3v = 0 Move all terms containing t to the left, all other terms to the right. Add '3v' to each side of the equation. 2t + -3v + 3v = 0 + 3v Combine like terms: -3v + 3v = 0 2t + 0 = 0 + 3v 2t = 0 + 3v Remove the zero: 2t = 3v Divide each side by '2'. t = 1.5v Simplifying t = 1.5vSubproblem 2
Set the factor '(5t + -6v)' equal to zero and attempt to solve: Simplifying 5t + -6v = 0 Solving 5t + -6v = 0 Move all terms containing t to the left, all other terms to the right. Add '6v' to each side of the equation. 5t + -6v + 6v = 0 + 6v Combine like terms: -6v + 6v = 0 5t + 0 = 0 + 6v 5t = 0 + 6v Remove the zero: 5t = 6v Divide each side by '5'. t = 1.2v Simplifying t = 1.2vSolution
t = {1.5v, 1.2v}
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