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Simplifying (2t + -1)(4t + 2) + (2t + -1)(t + 4) = 0 Reorder the terms: (-1 + 2t)(4t + 2) + (2t + -1)(t + 4) = 0 Reorder the terms: (-1 + 2t)(2 + 4t) + (2t + -1)(t + 4) = 0 Multiply (-1 + 2t) * (2 + 4t) (-1(2 + 4t) + 2t * (2 + 4t)) + (2t + -1)(t + 4) = 0 ((2 * -1 + 4t * -1) + 2t * (2 + 4t)) + (2t + -1)(t + 4) = 0 ((-2 + -4t) + 2t * (2 + 4t)) + (2t + -1)(t + 4) = 0 (-2 + -4t + (2 * 2t + 4t * 2t)) + (2t + -1)(t + 4) = 0 (-2 + -4t + (4t + 8t2)) + (2t + -1)(t + 4) = 0 Combine like terms: -4t + 4t = 0 (-2 + 0 + 8t2) + (2t + -1)(t + 4) = 0 (-2 + 8t2) + (2t + -1)(t + 4) = 0 Reorder the terms: -2 + 8t2 + (-1 + 2t)(t + 4) = 0 Reorder the terms: -2 + 8t2 + (-1 + 2t)(4 + t) = 0 Multiply (-1 + 2t) * (4 + t) -2 + 8t2 + (-1(4 + t) + 2t * (4 + t)) = 0 -2 + 8t2 + ((4 * -1 + t * -1) + 2t * (4 + t)) = 0 -2 + 8t2 + ((-4 + -1t) + 2t * (4 + t)) = 0 -2 + 8t2 + (-4 + -1t + (4 * 2t + t * 2t)) = 0 -2 + 8t2 + (-4 + -1t + (8t + 2t2)) = 0 Combine like terms: -1t + 8t = 7t -2 + 8t2 + (-4 + 7t + 2t2) = 0 Reorder the terms: -2 + -4 + 7t + 8t2 + 2t2 = 0 Combine like terms: -2 + -4 = -6 -6 + 7t + 8t2 + 2t2 = 0 Combine like terms: 8t2 + 2t2 = 10t2 -6 + 7t + 10t2 = 0 Solving -6 + 7t + 10t2 = 0 Solving for variable 't'. Factor a trinomial. (-6 + -5t)(1 + -2t) = 0Subproblem 1
Set the factor '(-6 + -5t)' equal to zero and attempt to solve: Simplifying -6 + -5t = 0 Solving -6 + -5t = 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 + -5t = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5t = 0 + 6 -5t = 0 + 6 Combine like terms: 0 + 6 = 6 -5t = 6 Divide each side by '-5'. t = -1.2 Simplifying t = -1.2Subproblem 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 = {-1.2, 0.5}
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