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Simplifying 6t4 + -28t3 + 16t2 = 0 Reorder the terms: 16t2 + -28t3 + 6t4 = 0 Solving 16t2 + -28t3 + 6t4 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2t2'. 2t2(8 + -14t + 3t2) = 0 Factor a trinomial. 2t2((2 + -3t)(4 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 't2' equal to zero and attempt to solve: Simplifying t2 = 0 Solving t2 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t2 = 0 Take the square root of each side: t = {0}Subproblem 2
Set the factor '(2 + -3t)' equal to zero and attempt to solve: Simplifying 2 + -3t = 0 Solving 2 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3t = 0 + -2 -3t = 0 + -2 Combine like terms: 0 + -2 = -2 -3t = -2 Divide each side by '-3'. t = 0.6666666667 Simplifying t = 0.6666666667Subproblem 3
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {0, 0.6666666667, 4}
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