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Simplifying 2t2 = -1tu + 6u2 Solving 2t2 = -1tu + 6u2 Solving for variable 't'. Reorder the terms: tu + 2t2 + -6u2 = -1tu + 6u2 + tu + -6u2 Reorder the terms: tu + 2t2 + -6u2 = -1tu + tu + 6u2 + -6u2 Combine like terms: -1tu + tu = 0 tu + 2t2 + -6u2 = 0 + 6u2 + -6u2 tu + 2t2 + -6u2 = 6u2 + -6u2 Combine like terms: 6u2 + -6u2 = 0 tu + 2t2 + -6u2 = 0 Factor a trinomial. (2t + -3u)(t + 2u) = 0Subproblem 1
Set the factor '(2t + -3u)' equal to zero and attempt to solve: Simplifying 2t + -3u = 0 Solving 2t + -3u = 0 Move all terms containing t to the left, all other terms to the right. Add '3u' to each side of the equation. 2t + -3u + 3u = 0 + 3u Combine like terms: -3u + 3u = 0 2t + 0 = 0 + 3u 2t = 0 + 3u Remove the zero: 2t = 3u Divide each side by '2'. t = 1.5u Simplifying t = 1.5uSubproblem 2
Set the factor '(t + 2u)' equal to zero and attempt to solve: Simplifying t + 2u = 0 Solving t + 2u = 0 Move all terms containing t to the left, all other terms to the right. Add '-2u' to each side of the equation. t + 2u + -2u = 0 + -2u Combine like terms: 2u + -2u = 0 t + 0 = 0 + -2u t = 0 + -2u Remove the zero: t = -2u Simplifying t = -2uSolution
t = {1.5u, -2u}
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