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Simplifying v(t) = t2 + -2t Multiply v * t tv = t2 + -2t Reorder the terms: tv = -2t + t2 Solving tv = -2t + t2 Solving for variable 't'. Reorder the terms: 2t + tv + -1t2 = -2t + t2 + 2t + -1t2 Reorder the terms: 2t + tv + -1t2 = -2t + 2t + t2 + -1t2 Combine like terms: -2t + 2t = 0 2t + tv + -1t2 = 0 + t2 + -1t2 2t + tv + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 2t + tv + -1t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(2 + v + -1t) = 0Subproblem 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 '(2 + v + -1t)' equal to zero and attempt to solve: Simplifying 2 + v + -1t = 0 Reorder the terms: 2 + -1t + v = 0 Solving 2 + -1t + v = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -1t + -2 + v = 0 + -2 Reorder the terms: 2 + -2 + -1t + v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t + v = 0 + -2 -1t + v = 0 + -2 Combine like terms: 0 + -2 = -2 -1t + v = -2 Add '-1v' to each side of the equation. -1t + v + -1v = -2 + -1v Combine like terms: v + -1v = 0 -1t + 0 = -2 + -1v -1t = -2 + -1v Divide each side by '-1'. t = 2 + v Simplifying t = 2 + vSolution
t = {0, 2 + v}
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