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Simplifying (13t + 7)(6t + -7) = 0 Reorder the terms: (7 + 13t)(6t + -7) = 0 Reorder the terms: (7 + 13t)(-7 + 6t) = 0 Multiply (7 + 13t) * (-7 + 6t) (7(-7 + 6t) + 13t * (-7 + 6t)) = 0 ((-7 * 7 + 6t * 7) + 13t * (-7 + 6t)) = 0 ((-49 + 42t) + 13t * (-7 + 6t)) = 0 (-49 + 42t + (-7 * 13t + 6t * 13t)) = 0 (-49 + 42t + (-91t + 78t2)) = 0 Combine like terms: 42t + -91t = -49t (-49 + -49t + 78t2) = 0 Solving -49 + -49t + 78t2 = 0 Solving for variable 't'. Factor a trinomial. (-7 + -13t)(7 + -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 '(7 + -6t)' equal to zero and attempt to solve: Simplifying 7 + -6t = 0 Solving 7 + -6t = 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 + -6t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6t = 0 + -7 -6t = 0 + -7 Combine like terms: 0 + -7 = -7 -6t = -7 Divide each side by '-6'. t = 1.166666667 Simplifying t = 1.166666667Solution
t = {-0.5384615385, 1.166666667}
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