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Simplifying (5t + -6)(5t + -6) + -13(5t + -6) + 36 = 0 Reorder the terms: (-6 + 5t)(5t + -6) + -13(5t + -6) + 36 = 0 Reorder the terms: (-6 + 5t)(-6 + 5t) + -13(5t + -6) + 36 = 0 Multiply (-6 + 5t) * (-6 + 5t) (-6(-6 + 5t) + 5t * (-6 + 5t)) + -13(5t + -6) + 36 = 0 ((-6 * -6 + 5t * -6) + 5t * (-6 + 5t)) + -13(5t + -6) + 36 = 0 ((36 + -30t) + 5t * (-6 + 5t)) + -13(5t + -6) + 36 = 0 (36 + -30t + (-6 * 5t + 5t * 5t)) + -13(5t + -6) + 36 = 0 (36 + -30t + (-30t + 25t2)) + -13(5t + -6) + 36 = 0 Combine like terms: -30t + -30t = -60t (36 + -60t + 25t2) + -13(5t + -6) + 36 = 0 Reorder the terms: 36 + -60t + 25t2 + -13(-6 + 5t) + 36 = 0 36 + -60t + 25t2 + (-6 * -13 + 5t * -13) + 36 = 0 36 + -60t + 25t2 + (78 + -65t) + 36 = 0 Reorder the terms: 36 + 78 + 36 + -60t + -65t + 25t2 = 0 Combine like terms: 36 + 78 = 114 114 + 36 + -60t + -65t + 25t2 = 0 Combine like terms: 114 + 36 = 150 150 + -60t + -65t + 25t2 = 0 Combine like terms: -60t + -65t = -125t 150 + -125t + 25t2 = 0 Solving 150 + -125t + 25t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '25'. 25(6 + -5t + t2) = 0 Factor a trinomial. 25((2 + -1t)(3 + -1t)) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {2, 3}
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