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Simplifying (3t2 + 6t) + (-9t2 + -5t + 5) = 0 Reorder the terms: (6t + 3t2) + (-9t2 + -5t + 5) = 0 Remove parenthesis around (6t + 3t2) 6t + 3t2 + (-9t2 + -5t + 5) = 0 Reorder the terms: 6t + 3t2 + (5 + -5t + -9t2) = 0 Remove parenthesis around (5 + -5t + -9t2) 6t + 3t2 + 5 + -5t + -9t2 = 0 Reorder the terms: 5 + 6t + -5t + 3t2 + -9t2 = 0 Combine like terms: 6t + -5t = 1t 5 + 1t + 3t2 + -9t2 = 0 Combine like terms: 3t2 + -9t2 = -6t2 5 + 1t + -6t2 = 0 Solving 5 + 1t + -6t2 = 0 Solving for variable 't'. Factor a trinomial. (1 + -1t)(5 + 6t) = 0Subproblem 1
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 = 1Subproblem 2
Set the factor '(5 + 6t)' equal to zero and attempt to solve: Simplifying 5 + 6t = 0 Solving 5 + 6t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 6t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6t = 0 + -5 6t = 0 + -5 Combine like terms: 0 + -5 = -5 6t = -5 Divide each side by '6'. t = -0.8333333333 Simplifying t = -0.8333333333Solution
t = {1, -0.8333333333}
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