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Simplifying (8t + 5)(3t + -4) = 0 Reorder the terms: (5 + 8t)(3t + -4) = 0 Reorder the terms: (5 + 8t)(-4 + 3t) = 0 Multiply (5 + 8t) * (-4 + 3t) (5(-4 + 3t) + 8t * (-4 + 3t)) = 0 ((-4 * 5 + 3t * 5) + 8t * (-4 + 3t)) = 0 ((-20 + 15t) + 8t * (-4 + 3t)) = 0 (-20 + 15t + (-4 * 8t + 3t * 8t)) = 0 (-20 + 15t + (-32t + 24t2)) = 0 Combine like terms: 15t + -32t = -17t (-20 + -17t + 24t2) = 0 Solving -20 + -17t + 24t2 = 0 Solving for variable 't'. Factor a trinomial. (-5 + -8t)(4 + -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 '(4 + -3t)' equal to zero and attempt to solve: Simplifying 4 + -3t = 0 Solving 4 + -3t = 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 + -3t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3t = 0 + -4 -3t = 0 + -4 Combine like terms: 0 + -4 = -4 -3t = -4 Divide each side by '-3'. t = 1.333333333 Simplifying t = 1.333333333Solution
t = {-0.625, 1.333333333}
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