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Simplifying 0 = 32t2 + 12t Reorder the terms: 0 = 12t + 32t2 Solving 0 = 12t + 32t2 Solving for variable 't'. Remove the zero: -12t + -32t2 = 12t + 32t2 + -12t + -32t2 Reorder the terms: -12t + -32t2 = 12t + -12t + 32t2 + -32t2 Combine like terms: 12t + -12t = 0 -12t + -32t2 = 0 + 32t2 + -32t2 -12t + -32t2 = 32t2 + -32t2 Combine like terms: 32t2 + -32t2 = 0 -12t + -32t2 = 0 Factor out the Greatest Common Factor (GCF), '-4t'. -4t(3 + 8t) = 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 '(3 + 8t)' equal to zero and attempt to solve: Simplifying 3 + 8t = 0 Solving 3 + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 8t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8t = 0 + -3 8t = 0 + -3 Combine like terms: 0 + -3 = -3 8t = -3 Divide each side by '8'. t = -0.375 Simplifying t = -0.375Solution
t = {0, -0.375}
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