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Simplifying (6t + 13)(t + 12) = 0 Reorder the terms: (13 + 6t)(t + 12) = 0 Reorder the terms: (13 + 6t)(12 + t) = 0 Multiply (13 + 6t) * (12 + t) (13(12 + t) + 6t * (12 + t)) = 0 ((12 * 13 + t * 13) + 6t * (12 + t)) = 0 ((156 + 13t) + 6t * (12 + t)) = 0 (156 + 13t + (12 * 6t + t * 6t)) = 0 (156 + 13t + (72t + 6t2)) = 0 Combine like terms: 13t + 72t = 85t (156 + 85t + 6t2) = 0 Solving 156 + 85t + 6t2 = 0 Solving for variable 't'. Factor a trinomial. (12 + t)(13 + 6t) = 0Subproblem 1
Set the factor '(12 + t)' equal to zero and attempt to solve: Simplifying 12 + t = 0 Solving 12 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + t = 0 + -12 Combine like terms: 12 + -12 = 0 0 + t = 0 + -12 t = 0 + -12 Combine like terms: 0 + -12 = -12 t = -12 Simplifying t = -12Subproblem 2
Set the factor '(13 + 6t)' equal to zero and attempt to solve: Simplifying 13 + 6t = 0 Solving 13 + 6t = 0 Move all terms containing t to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 6t = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 6t = 0 + -13 6t = 0 + -13 Combine like terms: 0 + -13 = -13 6t = -13 Divide each side by '6'. t = -2.166666667 Simplifying t = -2.166666667Solution
t = {-12, -2.166666667}
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