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Simplifying 8(t + -1t2) + -6(t + -1t2) = 0 (t * 8 + -1t2 * 8) + -6(t + -1t2) = 0 (8t + -8t2) + -6(t + -1t2) = 0 8t + -8t2 + (t * -6 + -1t2 * -6) = 0 8t + -8t2 + (-6t + 6t2) = 0 Reorder the terms: 8t + -6t + -8t2 + 6t2 = 0 Combine like terms: 8t + -6t = 2t 2t + -8t2 + 6t2 = 0 Combine like terms: -8t2 + 6t2 = -2t2 2t + -2t2 = 0 Solving 2t + -2t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2t'. 2t(1 + -1t) = 0 Ignore the factor 2.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {0, 1}
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