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Simplifying 4t2 + 80t + 24 = -276 Reorder the terms: 24 + 80t + 4t2 = -276 Solving 24 + 80t + 4t2 = -276 Solving for variable 't'. Reorder the terms: 24 + 276 + 80t + 4t2 = -276 + 276 Combine like terms: 24 + 276 = 300 300 + 80t + 4t2 = -276 + 276 Combine like terms: -276 + 276 = 0 300 + 80t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(75 + 20t + t2) = 0 Factor a trinomial. 4((15 + t)(5 + t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(15 + t)' equal to zero and attempt to solve: Simplifying 15 + t = 0 Solving 15 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + t = 0 + -15 Combine like terms: 15 + -15 = 0 0 + t = 0 + -15 t = 0 + -15 Combine like terms: 0 + -15 = -15 t = -15 Simplifying t = -15Subproblem 2
Set the factor '(5 + t)' equal to zero and attempt to solve: Simplifying 5 + t = 0 Solving 5 + t = 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 + t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + t = 0 + -5 t = 0 + -5 Combine like terms: 0 + -5 = -5 t = -5 Simplifying t = -5Solution
t = {-15, -5}
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