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Simplifying (4t + -5)(2t + -5) = 0 Reorder the terms: (-5 + 4t)(2t + -5) = 0 Reorder the terms: (-5 + 4t)(-5 + 2t) = 0 Multiply (-5 + 4t) * (-5 + 2t) (-5(-5 + 2t) + 4t * (-5 + 2t)) = 0 ((-5 * -5 + 2t * -5) + 4t * (-5 + 2t)) = 0 ((25 + -10t) + 4t * (-5 + 2t)) = 0 (25 + -10t + (-5 * 4t + 2t * 4t)) = 0 (25 + -10t + (-20t + 8t2)) = 0 Combine like terms: -10t + -20t = -30t (25 + -30t + 8t2) = 0 Solving 25 + -30t + 8t2 = 0 Solving for variable 't'. Factor a trinomial. (5 + -4t)(5 + -2t) = 0Subproblem 1
Set the factor '(5 + -4t)' equal to zero and attempt to solve: Simplifying 5 + -4t = 0 Solving 5 + -4t = 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 + -4t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4t = 0 + -5 -4t = 0 + -5 Combine like terms: 0 + -5 = -5 -4t = -5 Divide each side by '-4'. t = 1.25 Simplifying t = 1.25Subproblem 2
Set the factor '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 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 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5Solution
t = {1.25, 2.5}
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