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Simplifying 20t + -5 = 12t2 + 4t + -1 Reorder the terms: -5 + 20t = 12t2 + 4t + -1 Reorder the terms: -5 + 20t = -1 + 4t + 12t2 Solving -5 + 20t = -1 + 4t + 12t2 Solving for variable 't'. Reorder the terms: -5 + 1 + 20t + -4t + -12t2 = -1 + 4t + 12t2 + 1 + -4t + -12t2 Combine like terms: -5 + 1 = -4 -4 + 20t + -4t + -12t2 = -1 + 4t + 12t2 + 1 + -4t + -12t2 Combine like terms: 20t + -4t = 16t -4 + 16t + -12t2 = -1 + 4t + 12t2 + 1 + -4t + -12t2 Reorder the terms: -4 + 16t + -12t2 = -1 + 1 + 4t + -4t + 12t2 + -12t2 Combine like terms: -1 + 1 = 0 -4 + 16t + -12t2 = 0 + 4t + -4t + 12t2 + -12t2 -4 + 16t + -12t2 = 4t + -4t + 12t2 + -12t2 Combine like terms: 4t + -4t = 0 -4 + 16t + -12t2 = 0 + 12t2 + -12t2 -4 + 16t + -12t2 = 12t2 + -12t2 Combine like terms: 12t2 + -12t2 = 0 -4 + 16t + -12t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + 4t + -3t2) = 0 Factor a trinomial. 4((-1 + t)(1 + -3t)) = 0 Ignore the factor 4.Subproblem 1
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 = 1Subproblem 2
Set the factor '(1 + -3t)' equal to zero and attempt to solve: Simplifying 1 + -3t = 0 Solving 1 + -3t = 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 + -3t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3t = 0 + -1 -3t = 0 + -1 Combine like terms: 0 + -1 = -1 -3t = -1 Divide each side by '-3'. t = 0.3333333333 Simplifying t = 0.3333333333Solution
t = {1, 0.3333333333}
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