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Simplifying 0 = 4t2 + 5t + -21 Reorder the terms: 0 = -21 + 5t + 4t2 Solving 0 = -21 + 5t + 4t2 Solving for variable 't'. Combine like terms: 0 + 21 = 21 21 + -5t + -4t2 = -21 + 5t + 4t2 + 21 + -5t + -4t2 Reorder the terms: 21 + -5t + -4t2 = -21 + 21 + 5t + -5t + 4t2 + -4t2 Combine like terms: -21 + 21 = 0 21 + -5t + -4t2 = 0 + 5t + -5t + 4t2 + -4t2 21 + -5t + -4t2 = 5t + -5t + 4t2 + -4t2 Combine like terms: 5t + -5t = 0 21 + -5t + -4t2 = 0 + 4t2 + -4t2 21 + -5t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 21 + -5t + -4t2 = 0 Factor a trinomial. (7 + -4t)(3 + t) = 0Subproblem 1
Set the factor '(7 + -4t)' equal to zero and attempt to solve: Simplifying 7 + -4t = 0 Solving 7 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4t = 0 + -7 -4t = 0 + -7 Combine like terms: 0 + -7 = -7 -4t = -7 Divide each side by '-4'. t = 1.75 Simplifying t = 1.75Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve: Simplifying 3 + t = 0 Solving 3 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + t = 0 + -3 t = 0 + -3 Combine like terms: 0 + -3 = -3 t = -3 Simplifying t = -3Solution
t = {1.75, -3}
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