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Simplifying t(t + -2) + -3t(t + -2) = 0 Reorder the terms: t(-2 + t) + -3t(t + -2) = 0 (-2 * t + t * t) + -3t(t + -2) = 0 (-2t + t2) + -3t(t + -2) = 0 Reorder the terms: -2t + t2 + -3t(-2 + t) = 0 -2t + t2 + (-2 * -3t + t * -3t) = 0 -2t + t2 + (6t + -3t2) = 0 Reorder the terms: -2t + 6t + t2 + -3t2 = 0 Combine like terms: -2t + 6t = 4t 4t + t2 + -3t2 = 0 Combine like terms: t2 + -3t2 = -2t2 4t + -2t2 = 0 Solving 4t + -2t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2t'. 2t(2 + -1t) = 0 Ignore the factor 2.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 '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 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 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {0, 2}
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