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Simplifying 12t2 + 32t + 16 = 0 Reorder the terms: 16 + 32t + 12t2 = 0 Solving 16 + 32t + 12t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(4 + 8t + 3t2) = 0 Factor a trinomial. 4((2 + t)(2 + 3t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + t)' equal to zero and attempt to solve: Simplifying 2 + t = 0 Solving 2 + t = 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 + t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + t = 0 + -2 t = 0 + -2 Combine like terms: 0 + -2 = -2 t = -2 Simplifying t = -2Subproblem 2
Set the factor '(2 + 3t)' equal to zero and attempt to solve: Simplifying 2 + 3t = 0 Solving 2 + 3t = 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 + 3t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3t = 0 + -2 3t = 0 + -2 Combine like terms: 0 + -2 = -2 3t = -2 Divide each side by '3'. t = -0.6666666667 Simplifying t = -0.6666666667Solution
t = {-2, -0.6666666667}
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