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Simplifying 2(x + -2t) + 3(3x + 2t) + -4(x + -3t) = 0 Reorder the terms: 2(-2t + x) + 3(3x + 2t) + -4(x + -3t) = 0 (-2t * 2 + x * 2) + 3(3x + 2t) + -4(x + -3t) = 0 (-4t + 2x) + 3(3x + 2t) + -4(x + -3t) = 0 Reorder the terms: -4t + 2x + 3(2t + 3x) + -4(x + -3t) = 0 -4t + 2x + (2t * 3 + 3x * 3) + -4(x + -3t) = 0 -4t + 2x + (6t + 9x) + -4(x + -3t) = 0 Reorder the terms: -4t + 2x + 6t + 9x + -4(-3t + x) = 0 -4t + 2x + 6t + 9x + (-3t * -4 + x * -4) = 0 -4t + 2x + 6t + 9x + (12t + -4x) = 0 Reorder the terms: -4t + 6t + 12t + 2x + 9x + -4x = 0 Combine like terms: -4t + 6t = 2t 2t + 12t + 2x + 9x + -4x = 0 Combine like terms: 2t + 12t = 14t 14t + 2x + 9x + -4x = 0 Combine like terms: 2x + 9x = 11x 14t + 11x + -4x = 0 Combine like terms: 11x + -4x = 7x 14t + 7x = 0 Solving 14t + 7x = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7x' to each side of the equation. 14t + 7x + -7x = 0 + -7x Combine like terms: 7x + -7x = 0 14t + 0 = 0 + -7x 14t = 0 + -7x Remove the zero: 14t = -7x Divide each side by '14'. t = -0.5x Simplifying t = -0.5x
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