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Simplifying 16 = 12t + -2t2 Solving 16 = 12t + -2t2 Solving for variable 't'. Reorder the terms: 16 + -12t + 2t2 = 12t + -12t + -2t2 + 2t2 Combine like terms: 12t + -12t = 0 16 + -12t + 2t2 = 0 + -2t2 + 2t2 16 + -12t + 2t2 = -2t2 + 2t2 Combine like terms: -2t2 + 2t2 = 0 16 + -12t + 2t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -6t + t2) = 0 Factor a trinomial. 2((2 + -1t)(4 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 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 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {2, 4}
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