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Simplifying t = 3t(t + 5) Reorder the terms: t = 3t(5 + t) t = (5 * 3t + t * 3t) t = (15t + 3t2) Solving t = 15t + 3t2 Solving for variable 't'. Combine like terms: t + -15t = -14t -14t + -3t2 = 15t + 3t2 + -15t + -3t2 Reorder the terms: -14t + -3t2 = 15t + -15t + 3t2 + -3t2 Combine like terms: 15t + -15t = 0 -14t + -3t2 = 0 + 3t2 + -3t2 -14t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 -14t + -3t2 = 0 Factor out the Greatest Common Factor (GCF), '-1t'. -1t(14 + 3t) = 0 Ignore the factor -1.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 '(14 + 3t)' equal to zero and attempt to solve: Simplifying 14 + 3t = 0 Solving 14 + 3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + 3t = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 3t = 0 + -14 3t = 0 + -14 Combine like terms: 0 + -14 = -14 3t = -14 Divide each side by '3'. t = -4.666666667 Simplifying t = -4.666666667Solution
t = {0, -4.666666667}
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