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Simplifying 60v2 + -39vt + -45t2 = 0 Reorder the terms: -39tv + -45t2 + 60v2 = 0 Solving -39tv + -45t2 + 60v2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(-13tv + -15t2 + 20v2) = 0 Factor a trinomial. 3((-3t + -5v)(5t + -4v)) = 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 '(5t + -4v)' equal to zero and attempt to solve: Simplifying 5t + -4v = 0 Solving 5t + -4v = 0 Move all terms containing t to the left, all other terms to the right. Add '4v' to each side of the equation. 5t + -4v + 4v = 0 + 4v Combine like terms: -4v + 4v = 0 5t + 0 = 0 + 4v 5t = 0 + 4v Remove the zero: 5t = 4v Divide each side by '5'. t = 0.8v Simplifying t = 0.8vSolution
t = {-1.666666667v, 0.8v}
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