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Simplifying 6 = 16t2 + 36t + 6 Reorder the terms: 6 = 6 + 36t + 16t2 Add '-6' to each side of the equation. 6 + -6 = 6 + 36t + -6 + 16t2 Combine like terms: 6 + -6 = 0 0 = 6 + 36t + -6 + 16t2 Reorder the terms: 0 = 6 + -6 + 36t + 16t2 Combine like terms: 6 + -6 = 0 0 = 0 + 36t + 16t2 0 = 36t + 16t2 Solving 0 = 36t + 16t2 Solving for variable 't'. Remove the zero: -36t + -16t2 = 36t + 16t2 + -36t + -16t2 Reorder the terms: -36t + -16t2 = 36t + -36t + 16t2 + -16t2 Combine like terms: 36t + -36t = 0 -36t + -16t2 = 0 + 16t2 + -16t2 -36t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -36t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-4t'. -4t(9 + 4t) = 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 '(9 + 4t)' equal to zero and attempt to solve: Simplifying 9 + 4t = 0 Solving 9 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4t = 0 + -9 4t = 0 + -9 Combine like terms: 0 + -9 = -9 4t = -9 Divide each side by '4'. t = -2.25 Simplifying t = -2.25Solution
t = {0, -2.25}
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