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Simplifying 8t5 + 2t4 = 10t3 Reorder the terms: 2t4 + 8t5 = 10t3 Solving 2t4 + 8t5 = 10t3 Solving for variable 't'. Reorder the terms: -10t3 + 2t4 + 8t5 = 10t3 + -10t3 Combine like terms: 10t3 + -10t3 = 0 -10t3 + 2t4 + 8t5 = 0 Factor out the Greatest Common Factor (GCF), '2t3'. 2t3(-5 + t + 4t2) = 0 Factor a trinomial. 2t3((-5 + -4t)(1 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 't3' equal to zero and attempt to solve: Simplifying t3 = 0 Solving t3 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t3 = 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 '(-5 + -4t)' equal to zero and attempt to solve: Simplifying -5 + -4t = 0 Solving -5 + -4t = 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 + -4t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4t = 0 + 5 -4t = 0 + 5 Combine like terms: 0 + 5 = 5 -4t = 5 Divide each side by '-4'. t = -1.25 Simplifying t = -1.25Subproblem 3
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 = {-1.25, 1}
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