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Simplifying (13t + 7)(6t + -5) = 0 Reorder the terms: (7 + 13t)(6t + -5) = 0 Reorder the terms: (7 + 13t)(-5 + 6t) = 0 Multiply (7 + 13t) * (-5 + 6t) (7(-5 + 6t) + 13t * (-5 + 6t)) = 0 ((-5 * 7 + 6t * 7) + 13t * (-5 + 6t)) = 0 ((-35 + 42t) + 13t * (-5 + 6t)) = 0 (-35 + 42t + (-5 * 13t + 6t * 13t)) = 0 (-35 + 42t + (-65t + 78t2)) = 0 Combine like terms: 42t + -65t = -23t (-35 + -23t + 78t2) = 0 Solving -35 + -23t + 78t2 = 0 Solving for variable 't'. Factor a trinomial. (-7 + -13t)(5 + -6t) = 0Subproblem 1
Set the factor '(-7 + -13t)' equal to zero and attempt to solve: Simplifying -7 + -13t = 0 Solving -7 + -13t = 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 + -13t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -13t = 0 + 7 -13t = 0 + 7 Combine like terms: 0 + 7 = 7 -13t = 7 Divide each side by '-13'. t = -0.5384615385 Simplifying t = -0.5384615385Subproblem 2
Set the factor '(5 + -6t)' equal to zero and attempt to solve: Simplifying 5 + -6t = 0 Solving 5 + -6t = 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 + -6t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6t = 0 + -5 -6t = 0 + -5 Combine like terms: 0 + -5 = -5 -6t = -5 Divide each side by '-6'. t = 0.8333333333 Simplifying t = 0.8333333333Solution
t = {-0.5384615385, 0.8333333333}
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