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Simplifying 12t2 = 32 + 40t Solving 12t2 = 32 + 40t Solving for variable 't'. Reorder the terms: -32 + -40t + 12t2 = 32 + 40t + -32 + -40t Reorder the terms: -32 + -40t + 12t2 = 32 + -32 + 40t + -40t Combine like terms: 32 + -32 = 0 -32 + -40t + 12t2 = 0 + 40t + -40t -32 + -40t + 12t2 = 40t + -40t Combine like terms: 40t + -40t = 0 -32 + -40t + 12t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + -10t + 3t2) = 0 Factor a trinomial. 4((-2 + -3t)(4 + -1t)) = 0 Ignore the factor 4.Subproblem 1
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 2
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 = {-0.6666666667, 4}
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