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Simplifying 5[3(7 + -1t) + -4(8 + 2t)] + -20 = -6[2(6 + 3t) + -4] 5[(7 * 3 + -1t * 3) + -4(8 + 2t)] + -20 = -6[2(6 + 3t) + -4] 5[(21 + -3t) + -4(8 + 2t)] + -20 = -6[2(6 + 3t) + -4] 5[21 + -3t + (8 * -4 + 2t * -4)] + -20 = -6[2(6 + 3t) + -4] 5[21 + -3t + (-32 + -8t)] + -20 = -6[2(6 + 3t) + -4] Reorder the terms: 5[21 + -32 + -3t + -8t] + -20 = -6[2(6 + 3t) + -4] Combine like terms: 21 + -32 = -11 5[-11 + -3t + -8t] + -20 = -6[2(6 + 3t) + -4] Combine like terms: -3t + -8t = -11t 5[-11 + -11t] + -20 = -6[2(6 + 3t) + -4] [-11 * 5 + -11t * 5] + -20 = -6[2(6 + 3t) + -4] [-55 + -55t] + -20 = -6[2(6 + 3t) + -4] Reorder the terms: -55 + -20 + -55t = -6[2(6 + 3t) + -4] Combine like terms: -55 + -20 = -75 -75 + -55t = -6[2(6 + 3t) + -4] -75 + -55t = -6[(6 * 2 + 3t * 2) + -4] -75 + -55t = -6[(12 + 6t) + -4] Reorder the terms: -75 + -55t = -6[12 + -4 + 6t] Combine like terms: 12 + -4 = 8 -75 + -55t = -6[8 + 6t] -75 + -55t = [8 * -6 + 6t * -6] -75 + -55t = [-48 + -36t] Solving -75 + -55t = -48 + -36t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '36t' to each side of the equation. -75 + -55t + 36t = -48 + -36t + 36t Combine like terms: -55t + 36t = -19t -75 + -19t = -48 + -36t + 36t Combine like terms: -36t + 36t = 0 -75 + -19t = -48 + 0 -75 + -19t = -48 Add '75' to each side of the equation. -75 + 75 + -19t = -48 + 75 Combine like terms: -75 + 75 = 0 0 + -19t = -48 + 75 -19t = -48 + 75 Combine like terms: -48 + 75 = 27 -19t = 27 Divide each side by '-19'. t = -1.421052632 Simplifying t = -1.421052632
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