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Simplifying 12t4 + 40t3 + 32t2 = 0 Reorder the terms: 32t2 + 40t3 + 12t4 = 0 Solving 32t2 + 40t3 + 12t4 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4t2'. 4t2(8 + 10t + 3t2) = 0 Factor a trinomial. 4t2((2 + t)(4 + 3t)) = 0 Ignore the factor 4.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 + t)' equal to zero and attempt to solve: Simplifying 2 + t = 0 Solving 2 + t = 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 + t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + t = 0 + -2 t = 0 + -2 Combine like terms: 0 + -2 = -2 t = -2 Simplifying t = -2Subproblem 3
Set the factor '(4 + 3t)' equal to zero and attempt to solve: Simplifying 4 + 3t = 0 Solving 4 + 3t = 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 + 3t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3t = 0 + -4 3t = 0 + -4 Combine like terms: 0 + -4 = -4 3t = -4 Divide each side by '3'. t = -1.333333333 Simplifying t = -1.333333333Solution
t = {0, -2, -1.333333333}
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