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Simplifying 0 = 3t6 + -21t5 + -24t4 Reorder the terms: 0 = -24t4 + -21t5 + 3t6 Solving 0 = -24t4 + -21t5 + 3t6 Solving for variable 't'. Remove the zero: 24t4 + 21t5 + -3t6 = -24t4 + -21t5 + 3t6 + 24t4 + 21t5 + -3t6 Reorder the terms: 24t4 + 21t5 + -3t6 = -24t4 + 24t4 + -21t5 + 21t5 + 3t6 + -3t6 Combine like terms: -24t4 + 24t4 = 0 24t4 + 21t5 + -3t6 = 0 + -21t5 + 21t5 + 3t6 + -3t6 24t4 + 21t5 + -3t6 = -21t5 + 21t5 + 3t6 + -3t6 Combine like terms: -21t5 + 21t5 = 0 24t4 + 21t5 + -3t6 = 0 + 3t6 + -3t6 24t4 + 21t5 + -3t6 = 3t6 + -3t6 Combine like terms: 3t6 + -3t6 = 0 24t4 + 21t5 + -3t6 = 0 Factor out the Greatest Common Factor (GCF), '3t4'. 3t4(8 + 7t + -1t2) = 0 Factor a trinomial. 3t4((8 + -1t)(1 + t)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 't4' equal to zero and attempt to solve: Simplifying t4 = 0 Solving t4 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(8 + -1t)' equal to zero and attempt to solve: Simplifying 8 + -1t = 0 Solving 8 + -1t = 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 + -1t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1t = 0 + -8 -1t = 0 + -8 Combine like terms: 0 + -8 = -8 -1t = -8 Divide each side by '-1'. t = 8 Simplifying t = 8Subproblem 3
Set the factor '(1 + t)' equal to zero and attempt to solve: Simplifying 1 + t = 0 Solving 1 + t = 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 + t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + t = 0 + -1 t = 0 + -1 Combine like terms: 0 + -1 = -1 t = -1 Simplifying t = -1Solution
t = {8, -1}
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