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Simplifying 65t = 5t2 + 12t Reorder the terms: 65t = 12t + 5t2 Solving 65t = 12t + 5t2 Solving for variable 't'. Combine like terms: 65t + -12t = 53t 53t + -5t2 = 12t + 5t2 + -12t + -5t2 Reorder the terms: 53t + -5t2 = 12t + -12t + 5t2 + -5t2 Combine like terms: 12t + -12t = 0 53t + -5t2 = 0 + 5t2 + -5t2 53t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 53t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(53 + -5t) = 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 '(53 + -5t)' equal to zero and attempt to solve: Simplifying 53 + -5t = 0 Solving 53 + -5t = 0 Move all terms containing t to the left, all other terms to the right. Add '-53' to each side of the equation. 53 + -53 + -5t = 0 + -53 Combine like terms: 53 + -53 = 0 0 + -5t = 0 + -53 -5t = 0 + -53 Combine like terms: 0 + -53 = -53 -5t = -53 Divide each side by '-5'. t = 10.6 Simplifying t = 10.6Solution
t = {0, 10.6}
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