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Simplifying (11t + 6)(5t + -15) = 0 Reorder the terms: (6 + 11t)(5t + -15) = 0 Reorder the terms: (6 + 11t)(-15 + 5t) = 0 Multiply (6 + 11t) * (-15 + 5t) (6(-15 + 5t) + 11t * (-15 + 5t)) = 0 ((-15 * 6 + 5t * 6) + 11t * (-15 + 5t)) = 0 ((-90 + 30t) + 11t * (-15 + 5t)) = 0 (-90 + 30t + (-15 * 11t + 5t * 11t)) = 0 (-90 + 30t + (-165t + 55t2)) = 0 Combine like terms: 30t + -165t = -135t (-90 + -135t + 55t2) = 0 Solving -90 + -135t + 55t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(-18 + -27t + 11t2) = 0 Factor a trinomial. 5((-6 + -11t)(3 + -1t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-6 + -11t)' equal to zero and attempt to solve: Simplifying -6 + -11t = 0 Solving -6 + -11t = 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 + -11t = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -11t = 0 + 6 -11t = 0 + 6 Combine like terms: 0 + 6 = 6 -11t = 6 Divide each side by '-11'. t = -0.5454545455 Simplifying t = -0.5454545455Subproblem 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 = {-0.5454545455, 3}
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