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Simplifying (8t + 5)(3t + -5) = 0 Reorder the terms: (5 + 8t)(3t + -5) = 0 Reorder the terms: (5 + 8t)(-5 + 3t) = 0 Multiply (5 + 8t) * (-5 + 3t) (5(-5 + 3t) + 8t * (-5 + 3t)) = 0 ((-5 * 5 + 3t * 5) + 8t * (-5 + 3t)) = 0 ((-25 + 15t) + 8t * (-5 + 3t)) = 0 (-25 + 15t + (-5 * 8t + 3t * 8t)) = 0 (-25 + 15t + (-40t + 24t2)) = 0 Combine like terms: 15t + -40t = -25t (-25 + -25t + 24t2) = 0 Solving -25 + -25t + 24t2 = 0 Solving for variable 't'. Factor a trinomial. (-5 + -8t)(5 + -3t) = 0Subproblem 1
Set the factor '(-5 + -8t)' equal to zero and attempt to solve: Simplifying -5 + -8t = 0 Solving -5 + -8t = 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 + -8t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8t = 0 + 5 -8t = 0 + 5 Combine like terms: 0 + 5 = 5 -8t = 5 Divide each side by '-8'. t = -0.625 Simplifying t = -0.625Subproblem 2
Set the factor '(5 + -3t)' equal to zero and attempt to solve: Simplifying 5 + -3t = 0 Solving 5 + -3t = 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 + -3t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3t = 0 + -5 -3t = 0 + -5 Combine like terms: 0 + -5 = -5 -3t = -5 Divide each side by '-3'. t = 1.666666667 Simplifying t = 1.666666667Solution
t = {-0.625, 1.666666667}
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