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Simplifying (9t + -4)(-9t + -5) = 0 Reorder the terms: (-4 + 9t)(-9t + -5) = 0 Reorder the terms: (-4 + 9t)(-5 + -9t) = 0 Multiply (-4 + 9t) * (-5 + -9t) (-4(-5 + -9t) + 9t * (-5 + -9t)) = 0 ((-5 * -4 + -9t * -4) + 9t * (-5 + -9t)) = 0 ((20 + 36t) + 9t * (-5 + -9t)) = 0 (20 + 36t + (-5 * 9t + -9t * 9t)) = 0 (20 + 36t + (-45t + -81t2)) = 0 Combine like terms: 36t + -45t = -9t (20 + -9t + -81t2) = 0 Solving 20 + -9t + -81t2 = 0 Solving for variable 't'. Factor a trinomial. (4 + -9t)(5 + 9t) = 0Subproblem 1
Set the factor '(4 + -9t)' equal to zero and attempt to solve: Simplifying 4 + -9t = 0 Solving 4 + -9t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -9t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9t = 0 + -4 -9t = 0 + -4 Combine like terms: 0 + -4 = -4 -9t = -4 Divide each side by '-9'. t = 0.4444444444 Simplifying t = 0.4444444444Subproblem 2
Set the factor '(5 + 9t)' equal to zero and attempt to solve: Simplifying 5 + 9t = 0 Solving 5 + 9t = 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 + 9t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 9t = 0 + -5 9t = 0 + -5 Combine like terms: 0 + -5 = -5 9t = -5 Divide each side by '9'. t = -0.5555555556 Simplifying t = -0.5555555556Solution
t = {0.4444444444, -0.5555555556}
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