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Simplifying (3t2) + 6t + -101 = 4 Reorder the terms: -101 + 6t + (3t2) = 4 Solving -101 + 6t + (3t2) = 4 Solving for variable 't'. Reorder the terms: -101 + -4 + 6t + (3t2) = 4 + -4 Combine like terms: -101 + -4 = -105 -105 + 6t + (3t2) = 4 + -4 Combine like terms: 4 + -4 = 0 -105 + 6t + (3t2) = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-35 + 2t + t2) = 0 Factor a trinomial. 3((-7 + -1t)(5 + -1t)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -1t)' equal to zero and attempt to solve: Simplifying -7 + -1t = 0 Solving -7 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1t = 0 + 7 -1t = 0 + 7 Combine like terms: 0 + 7 = 7 -1t = 7 Divide each side by '-1'. t = -7 Simplifying t = -7Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Solution
t = {-7, 5}
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