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Simplifying 4t2(t + 3(1 + 4ln(t))) = 0 Multiply ln * t 4t2(t + 3(1 + 4lnt)) = 0 4t2(t + (1 * 3 + 4lnt * 3)) = 0 4t2(t + (3 + 12lnt)) = 0 Reorder the terms: 4t2(3 + 12lnt + t) = 0 (3 * 4t2 + 12lnt * 4t2 + t * 4t2) = 0 Reorder the terms: (48lnt3 + 12t2 + 4t3) = 0 (48lnt3 + 12t2 + 4t3) = 0 Solving 48lnt3 + 12t2 + 4t3 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12t2' to each side of the equation. 48lnt3 + 12t2 + -12t2 + 4t3 = 0 + -12t2 Combine like terms: 12t2 + -12t2 = 0 48lnt3 + 0 + 4t3 = 0 + -12t2 48lnt3 + 4t3 = 0 + -12t2 Remove the zero: 48lnt3 + 4t3 = -12t2 Add '-4t3' to each side of the equation. 48lnt3 + 4t3 + -4t3 = -12t2 + -4t3 Combine like terms: 4t3 + -4t3 = 0 48lnt3 + 0 = -12t2 + -4t3 48lnt3 = -12t2 + -4t3 Divide each side by '48nt3'. l = -0.25n-1t-1 + -0.08333333333n-1 Simplifying l = -0.25n-1t-1 + -0.08333333333n-1 Reorder the terms: l = -0.08333333333n-1 + -0.25n-1t-1
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