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Simplifying 0 = 9t2 + 12t + 4 Reorder the terms: 0 = 4 + 12t + 9t2 Solving 0 = 4 + 12t + 9t2 Solving for variable 't'. Combine like terms: 0 + -4 = -4 -4 + -12t + -9t2 = 4 + 12t + 9t2 + -4 + -12t + -9t2 Reorder the terms: -4 + -12t + -9t2 = 4 + -4 + 12t + -12t + 9t2 + -9t2 Combine like terms: 4 + -4 = 0 -4 + -12t + -9t2 = 0 + 12t + -12t + 9t2 + -9t2 -4 + -12t + -9t2 = 12t + -12t + 9t2 + -9t2 Combine like terms: 12t + -12t = 0 -4 + -12t + -9t2 = 0 + 9t2 + -9t2 -4 + -12t + -9t2 = 9t2 + -9t2 Combine like terms: 9t2 + -9t2 = 0 -4 + -12t + -9t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 12t + 9t2) = 0 Factor a trinomial. -1((2 + 3t)(2 + 3t)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 3t)' equal to zero and attempt to solve: Simplifying 2 + 3t = 0 Solving 2 + 3t = 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 + 3t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3t = 0 + -2 3t = 0 + -2 Combine like terms: 0 + -2 = -2 3t = -2 Divide each side by '3'. t = -0.6666666667 Simplifying t = -0.6666666667Subproblem 2
Set the factor '(2 + 3t)' equal to zero and attempt to solve: Simplifying 2 + 3t = 0 Solving 2 + 3t = 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 + 3t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3t = 0 + -2 3t = 0 + -2 Combine like terms: 0 + -2 = -2 3t = -2 Divide each side by '3'. t = -0.6666666667 Simplifying t = -0.6666666667Solution
t = {-0.6666666667, -0.6666666667}
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