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Simplifying 3t(t + -5) + 6t * t = 0 Reorder the terms: 3t(-5 + t) + 6t * t = 0 (-5 * 3t + t * 3t) + 6t * t = 0 (-15t + 3t2) + 6t * t = 0 Multiply t * t -15t + 3t2 + 6t2 = 0 Combine like terms: 3t2 + 6t2 = 9t2 -15t + 9t2 = 0 Solving -15t + 9t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3t'. 3t(-5 + 3t) = 0 Ignore the factor 3.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 '(-5 + 3t)' equal to zero and attempt to solve: Simplifying -5 + 3t = 0 Solving -5 + 3t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 3t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3t = 0 + 5 3t = 0 + 5 Combine like terms: 0 + 5 = 5 3t = 5 Divide each side by '3'. t = 1.666666667 Simplifying t = 1.666666667Solution
t = {0, 1.666666667}
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