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Simplifying (-3t + -3v)(-7t + -5v) = 0 Multiply (-3t + -3v) * (-7t + -5v) (-3t * (-7t + -5v) + -3v * (-7t + -5v)) = 0 ((-7t * -3t + -5v * -3t) + -3v * (-7t + -5v)) = 0 Reorder the terms: ((15tv + 21t2) + -3v * (-7t + -5v)) = 0 ((15tv + 21t2) + -3v * (-7t + -5v)) = 0 (15tv + 21t2 + (-7t * -3v + -5v * -3v)) = 0 (15tv + 21t2 + (21tv + 15v2)) = 0 Reorder the terms: (15tv + 21tv + 21t2 + 15v2) = 0 Combine like terms: 15tv + 21tv = 36tv (36tv + 21t2 + 15v2) = 0 Solving 36tv + 21t2 + 15v2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(12tv + 7t2 + 5v2) = 0 Factor a trinomial. 3((7t + 5v)(t + v)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7t + 5v)' equal to zero and attempt to solve: Simplifying 7t + 5v = 0 Solving 7t + 5v = 0 Move all terms containing t to the left, all other terms to the right. Add '-5v' to each side of the equation. 7t + 5v + -5v = 0 + -5v Combine like terms: 5v + -5v = 0 7t + 0 = 0 + -5v 7t = 0 + -5v Remove the zero: 7t = -5v Divide each side by '7'. t = -0.7142857143v Simplifying t = -0.7142857143vSubproblem 2
Set the factor '(t + v)' equal to zero and attempt to solve: Simplifying t + v = 0 Solving t + v = 0 Move all terms containing t to the left, all other terms to the right. Add '-1v' to each side of the equation. t + v + -1v = 0 + -1v Combine like terms: v + -1v = 0 t + 0 = 0 + -1v t = 0 + -1v Remove the zero: t = -1v Simplifying t = -1vSolution
t = {-0.7142857143v, -1v}
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