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Simplifying 6t * 6t + 3t + -4t * 4t + 5t = 0 Reorder the terms for easier multiplication: 6 * 6t * t + 3t + -4t * 4t + 5t = 0 Multiply 6 * 6 36t * t + 3t + -4t * 4t + 5t = 0 Multiply t * t 36t2 + 3t + -4t * 4t + 5t = 0 Reorder the terms for easier multiplication: 36t2 + 3t + -4 * 4t * t + 5t = 0 Multiply -4 * 4 36t2 + 3t + -16t * t + 5t = 0 Multiply t * t 36t2 + 3t + -16t2 + 5t = 0 Reorder the terms: 3t + 5t + 36t2 + -16t2 = 0 Combine like terms: 3t + 5t = 8t 8t + 36t2 + -16t2 = 0 Combine like terms: 36t2 + -16t2 = 20t2 8t + 20t2 = 0 Solving 8t + 20t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4t'. 4t(2 + 5t) = 0 Ignore the factor 4.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 + 5t)' equal to zero and attempt to solve: Simplifying 2 + 5t = 0 Solving 2 + 5t = 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 + 5t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5t = 0 + -2 5t = 0 + -2 Combine like terms: 0 + -2 = -2 5t = -2 Divide each side by '5'. t = -0.4 Simplifying t = -0.4Solution
t = {0, -0.4}
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