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Simplifying 2x(2 + 4x + 2t) = 0 Reorder the terms: 2x(2 + 2t + 4x) = 0 (2 * 2x + 2t * 2x + 4x * 2x) = 0 Reorder the terms: (4tx + 4x + 8x2) = 0 (4tx + 4x + 8x2) = 0 Solving 4tx + 4x + 8x2 = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4x' to each side of the equation. 4tx + 4x + -4x + 8x2 = 0 + -4x Combine like terms: 4x + -4x = 0 4tx + 0 + 8x2 = 0 + -4x 4tx + 8x2 = 0 + -4x Remove the zero: 4tx + 8x2 = -4x Add '-8x2' to each side of the equation. 4tx + 8x2 + -8x2 = -4x + -8x2 Combine like terms: 8x2 + -8x2 = 0 4tx + 0 = -4x + -8x2 4tx = -4x + -8x2 Divide each side by '4x'. t = -1 + -2x Simplifying t = -1 + -2x
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