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Simplifying 3t2 + t = 24 Reorder the terms: t + 3t2 = 24 Solving t + 3t2 = 24 Solving for variable 't'. Reorder the terms: -24 + t + 3t2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + t + 3t2 = 0 Factor a trinomial. (-3 + -1t)(8 + -3t) = 0Subproblem 1
Set the factor '(-3 + -1t)' equal to zero and attempt to solve: Simplifying -3 + -1t = 0 Solving -3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1t = 0 + 3 -1t = 0 + 3 Combine like terms: 0 + 3 = 3 -1t = 3 Divide each side by '-1'. t = -3 Simplifying t = -3Subproblem 2
Set the factor '(8 + -3t)' equal to zero and attempt to solve: Simplifying 8 + -3t = 0 Solving 8 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3t = 0 + -8 -3t = 0 + -8 Combine like terms: 0 + -8 = -8 -3t = -8 Divide each side by '-3'. t = 2.666666667 Simplifying t = 2.666666667Solution
t = {-3, 2.666666667}
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