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Simplifying -6(7t + 8) + -1(3t + 4) + -2t + 12 = 0 Reorder the terms: -6(8 + 7t) + -1(3t + 4) + -2t + 12 = 0 (8 * -6 + 7t * -6) + -1(3t + 4) + -2t + 12 = 0 (-48 + -42t) + -1(3t + 4) + -2t + 12 = 0 Reorder the terms: -48 + -42t + -1(4 + 3t) + -2t + 12 = 0 -48 + -42t + (4 * -1 + 3t * -1) + -2t + 12 = 0 -48 + -42t + (-4 + -3t) + -2t + 12 = 0 Reorder the terms: -48 + -4 + 12 + -42t + -3t + -2t = 0 Combine like terms: -48 + -4 = -52 -52 + 12 + -42t + -3t + -2t = 0 Combine like terms: -52 + 12 = -40 -40 + -42t + -3t + -2t = 0 Combine like terms: -42t + -3t = -45t -40 + -45t + -2t = 0 Combine like terms: -45t + -2t = -47t -40 + -47t = 0 Solving -40 + -47t = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + -47t = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -47t = 0 + 40 -47t = 0 + 40 Combine like terms: 0 + 40 = 40 -47t = 40 Divide each side by '-47'. t = -0.8510638298 Simplifying t = -0.8510638298
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