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Simplifying (21t + 7)(9t + 1) = 0 Reorder the terms: (7 + 21t)(9t + 1) = 0 Reorder the terms: (7 + 21t)(1 + 9t) = 0 Multiply (7 + 21t) * (1 + 9t) (7(1 + 9t) + 21t * (1 + 9t)) = 0 ((1 * 7 + 9t * 7) + 21t * (1 + 9t)) = 0 ((7 + 63t) + 21t * (1 + 9t)) = 0 (7 + 63t + (1 * 21t + 9t * 21t)) = 0 (7 + 63t + (21t + 189t2)) = 0 Combine like terms: 63t + 21t = 84t (7 + 84t + 189t2) = 0 Solving 7 + 84t + 189t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '7'. 7(1 + 12t + 27t2) = 0 Factor a trinomial. 7((1 + 3t)(1 + 9t)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + 3t)' equal to zero and attempt to solve: Simplifying 1 + 3t = 0 Solving 1 + 3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3t = 0 + -1 3t = 0 + -1 Combine like terms: 0 + -1 = -1 3t = -1 Divide each side by '3'. t = -0.3333333333 Simplifying t = -0.3333333333Subproblem 2
Set the factor '(1 + 9t)' equal to zero and attempt to solve: Simplifying 1 + 9t = 0 Solving 1 + 9t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 9t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 9t = 0 + -1 9t = 0 + -1 Combine like terms: 0 + -1 = -1 9t = -1 Divide each side by '9'. t = -0.1111111111 Simplifying t = -0.1111111111Solution
t = {-0.3333333333, -0.1111111111}
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