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Simplifying t(t + -6)(3t + -11) = 0 Reorder the terms: t(-6 + t)(3t + -11) = 0 Reorder the terms: t(-6 + t)(-11 + 3t) = 0 Multiply (-6 + t) * (-11 + 3t) t(-6(-11 + 3t) + t(-11 + 3t)) = 0 t((-11 * -6 + 3t * -6) + t(-11 + 3t)) = 0 t((66 + -18t) + t(-11 + 3t)) = 0 t(66 + -18t + (-11 * t + 3t * t)) = 0 t(66 + -18t + (-11t + 3t2)) = 0 Combine like terms: -18t + -11t = -29t t(66 + -29t + 3t2) = 0 (66 * t + -29t * t + 3t2 * t) = 0 (66t + -29t2 + 3t3) = 0 Solving 66t + -29t2 + 3t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(66 + -29t + 3t2) = 0 Factor a trinomial. t((11 + -3t)(6 + -1t)) = 0Subproblem 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 '(11 + -3t)' equal to zero and attempt to solve: Simplifying 11 + -3t = 0 Solving 11 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -3t = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -3t = 0 + -11 -3t = 0 + -11 Combine like terms: 0 + -11 = -11 -3t = -11 Divide each side by '-3'. t = 3.666666667 Simplifying t = 3.666666667Subproblem 3
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, 3.666666667, 6}
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