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Simplifying 12t2 + -23t + -24 = 0 Reorder the terms: -24 + -23t + 12t2 = 0 Solving -24 + -23t + 12t2 = 0 Solving for variable 't'. Factor a trinomial. (-3 + -4t)(8 + -3t) = 0Subproblem 1
Set the factor '(-3 + -4t)' equal to zero and attempt to solve: Simplifying -3 + -4t = 0 Solving -3 + -4t = 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 + -4t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4t = 0 + 3 -4t = 0 + 3 Combine like terms: 0 + 3 = 3 -4t = 3 Divide each side by '-4'. t = -0.75 Simplifying t = -0.75Subproblem 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 = {-0.75, 2.666666667}
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