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Simplifying (4t + 9)(t + -8) = 0 Reorder the terms: (9 + 4t)(t + -8) = 0 Reorder the terms: (9 + 4t)(-8 + t) = 0 Multiply (9 + 4t) * (-8 + t) (9(-8 + t) + 4t * (-8 + t)) = 0 ((-8 * 9 + t * 9) + 4t * (-8 + t)) = 0 ((-72 + 9t) + 4t * (-8 + t)) = 0 (-72 + 9t + (-8 * 4t + t * 4t)) = 0 (-72 + 9t + (-32t + 4t2)) = 0 Combine like terms: 9t + -32t = -23t (-72 + -23t + 4t2) = 0 Solving -72 + -23t + 4t2 = 0 Solving for variable 't'. Factor a trinomial. (-9 + -4t)(8 + -1t) = 0Subproblem 1
Set the factor '(-9 + -4t)' equal to zero and attempt to solve: Simplifying -9 + -4t = 0 Solving -9 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -4t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4t = 0 + 9 -4t = 0 + 9 Combine like terms: 0 + 9 = 9 -4t = 9 Divide each side by '-4'. t = -2.25 Simplifying t = -2.25Subproblem 2
Set the factor '(8 + -1t)' equal to zero and attempt to solve: Simplifying 8 + -1t = 0 Solving 8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1t = 0 + -8 -1t = 0 + -8 Combine like terms: 0 + -8 = -8 -1t = -8 Divide each side by '-1'. t = 8 Simplifying t = 8Solution
t = {-2.25, 8}
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