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Simplifying t(3t + 2) + -6(3t + 2) = 0 Reorder the terms: t(2 + 3t) + -6(3t + 2) = 0 (2 * t + 3t * t) + -6(3t + 2) = 0 (2t + 3t2) + -6(3t + 2) = 0 Reorder the terms: 2t + 3t2 + -6(2 + 3t) = 0 2t + 3t2 + (2 * -6 + 3t * -6) = 0 2t + 3t2 + (-12 + -18t) = 0 Reorder the terms: -12 + 2t + -18t + 3t2 = 0 Combine like terms: 2t + -18t = -16t -12 + -16t + 3t2 = 0 Solving -12 + -16t + 3t2 = 0 Solving for variable 't'. Factor a trinomial. (-2 + -3t)(6 + -1t) = 0Subproblem 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 '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6Solution
t = {-0.6666666667, 6}
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