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Simplifying 3((-4 + -1t)(1 + -2t)) = 0 Multiply (-4 + -1t) * (1 + -2t) 3((-4(1 + -2t) + -1t * (1 + -2t))) = 0 3(((1 * -4 + -2t * -4) + -1t * (1 + -2t))) = 0 3(((-4 + 8t) + -1t * (1 + -2t))) = 0 3((-4 + 8t + (1 * -1t + -2t * -1t))) = 0 3((-4 + 8t + (-1t + 2t2))) = 0 Combine like terms: 8t + -1t = 7t 3((-4 + 7t + 2t2)) = 0 (-4 * 3 + 7t * 3 + 2t2 * 3) = 0 (-12 + 21t + 6t2) = 0 Solving -12 + 21t + 6t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 7t + 2t2) = 0 Factor a trinomial. 3((-4 + -1t)(1 + -2t)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -1t)' equal to zero and attempt to solve: Simplifying -4 + -1t = 0 Solving -4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1t = 0 + 4 -1t = 0 + 4 Combine like terms: 0 + 4 = 4 -1t = 4 Divide each side by '-1'. t = -4 Simplifying t = -4Subproblem 2
Set the factor '(1 + -2t)' equal to zero and attempt to solve: Simplifying 1 + -2t = 0 Solving 1 + -2t = 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 + -2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2t = 0 + -1 -2t = 0 + -1 Combine like terms: 0 + -1 = -1 -2t = -1 Divide each side by '-2'. t = 0.5 Simplifying t = 0.5Solution
t = {-4, 0.5}
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