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Simplifying (4t + -5)(t + 8) = 0 Reorder the terms: (-5 + 4t)(t + 8) = 0 Reorder the terms: (-5 + 4t)(8 + t) = 0 Multiply (-5 + 4t) * (8 + t) (-5(8 + t) + 4t * (8 + t)) = 0 ((8 * -5 + t * -5) + 4t * (8 + t)) = 0 ((-40 + -5t) + 4t * (8 + t)) = 0 (-40 + -5t + (8 * 4t + t * 4t)) = 0 (-40 + -5t + (32t + 4t2)) = 0 Combine like terms: -5t + 32t = 27t (-40 + 27t + 4t2) = 0 Solving -40 + 27t + 4t2 = 0 Solving for variable 't'. Factor a trinomial. (-8 + -1t)(5 + -4t) = 0Subproblem 1
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 = -8Subproblem 2
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 = 1.25Solution
t = {-8, 1.25}
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