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Simplifying 42t^{2}+ -13tv + -42v^{2}= 0 Reorder the terms: -13tv + 42t^{2}+ -42v^{2}= 0 Solving -13tv + 42t^{2}+ -42v^{2}= 0 Solving for variable 't'. Factor a trinomial. (6t + -7v)(7t + 6v) = 0## Subproblem 1

Set the factor '(6t + -7v)' equal to zero and attempt to solve: Simplifying 6t + -7v = 0 Solving 6t + -7v = 0 Move all terms containing t to the left, all other terms to the right. Add '7v' to each side of the equation. 6t + -7v + 7v = 0 + 7v Combine like terms: -7v + 7v = 0 6t + 0 = 0 + 7v 6t = 0 + 7v Remove the zero: 6t = 7v Divide each side by '6'. t = 1.166666667v Simplifying t = 1.166666667v## Subproblem 2

Set the factor '(7t + 6v)' equal to zero and attempt to solve: Simplifying 7t + 6v = 0 Solving 7t + 6v = 0 Move all terms containing t to the left, all other terms to the right. Add '-6v' to each side of the equation. 7t + 6v + -6v = 0 + -6v Combine like terms: 6v + -6v = 0 7t + 0 = 0 + -6v 7t = 0 + -6v Remove the zero: 7t = -6v Divide each side by '7'. t = -0.8571428571v Simplifying t = -0.8571428571v## Solution

t = {1.166666667v, -0.8571428571v}

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