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Simplifying 67 = 67 + -5t + -5t2 Add '-67' to each side of the equation. 67 + -67 = 67 + -5t + -67 + -5t2 Combine like terms: 67 + -67 = 0 0 = 67 + -5t + -67 + -5t2 Reorder the terms: 0 = 67 + -67 + -5t + -5t2 Combine like terms: 67 + -67 = 0 0 = 0 + -5t + -5t2 0 = -5t + -5t2 Solving 0 = -5t + -5t2 Solving for variable 't'. Remove the zero: 5t + 5t2 = -5t + -5t2 + 5t + 5t2 Reorder the terms: 5t + 5t2 = -5t + 5t + -5t2 + 5t2 Combine like terms: -5t + 5t = 0 5t + 5t2 = 0 + -5t2 + 5t2 5t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 5t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5t'. 5t(1 + t) = 0 Ignore the factor 5.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
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 = -1Solution
t = {0, -1}
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