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Simplifying t2 + 12tz + 32z2 = 0 Reorder the terms: 12tz + t2 + 32z2 = 0 Solving 12tz + t2 + 32z2 = 0 Solving for variable 't'. Factor a trinomial. (t + 4z)(t + 8z) = 0Subproblem 1
Set the factor '(t + 4z)' equal to zero and attempt to solve: Simplifying t + 4z = 0 Solving t + 4z = 0 Move all terms containing t to the left, all other terms to the right. Add '-4z' to each side of the equation. t + 4z + -4z = 0 + -4z Combine like terms: 4z + -4z = 0 t + 0 = 0 + -4z t = 0 + -4z Remove the zero: t = -4z Simplifying t = -4zSubproblem 2
Set the factor '(t + 8z)' equal to zero and attempt to solve: Simplifying t + 8z = 0 Solving t + 8z = 0 Move all terms containing t to the left, all other terms to the right. Add '-8z' to each side of the equation. t + 8z + -8z = 0 + -8z Combine like terms: 8z + -8z = 0 t + 0 = 0 + -8z t = 0 + -8z Remove the zero: t = -8z Simplifying t = -8zSolution
t = {-4z, -8z}
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