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Simplifying 6t2 + -4t = 32 Reorder the terms: -4t + 6t2 = 32 Solving -4t + 6t2 = 32 Solving for variable 't'. Reorder the terms: -32 + -4t + 6t2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + -4t + 6t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + -2t + 3t2) = 0 Factor a trinomial. 2((-2 + -1t)(8 + -3t)) = 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 '(8 + -3t)' equal to zero and attempt to solve: Simplifying 8 + -3t = 0 Solving 8 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3t = 0 + -8 -3t = 0 + -8 Combine like terms: 0 + -8 = -8 -3t = -8 Divide each side by '-3'. t = 2.666666667 Simplifying t = 2.666666667Solution
t = {-2, 2.666666667}
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