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Simplifying (4t2 + -12t + 9) + (-16t + -24) + 15 = 0 Reorder the terms: (9 + -12t + 4t2) + (-16t + -24) + 15 = 0 Remove parenthesis around (9 + -12t + 4t2) 9 + -12t + 4t2 + (-16t + -24) + 15 = 0 Reorder the terms: 9 + -12t + 4t2 + (-24 + -16t) + 15 = 0 Remove parenthesis around (-24 + -16t) 9 + -12t + 4t2 + -24 + -16t + 15 = 0 Reorder the terms: 9 + -24 + 15 + -12t + -16t + 4t2 = 0 Combine like terms: 9 + -24 = -15 -15 + 15 + -12t + -16t + 4t2 = 0 Combine like terms: -15 + 15 = 0 0 + -12t + -16t + 4t2 = 0 -12t + -16t + 4t2 = 0 Combine like terms: -12t + -16t = -28t -28t + 4t2 = 0 Solving -28t + 4t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4t'. 4t(-7 + t) = 0 Ignore the factor 4.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-7 + t)' equal to zero and attempt to solve: Simplifying -7 + t = 0 Solving -7 + t = 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 + t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + t = 0 + 7 t = 0 + 7 Combine like terms: 0 + 7 = 7 t = 7 Simplifying t = 7Solution
t = {0, 7}
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