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Simplifying 3(3t + -5) = 5[-3t + -3(t + 9)] Reorder the terms: 3(-5 + 3t) = 5[-3t + -3(t + 9)] (-5 * 3 + 3t * 3) = 5[-3t + -3(t + 9)] (-15 + 9t) = 5[-3t + -3(t + 9)] Reorder the terms: -15 + 9t = 5[-3t + -3(9 + t)] -15 + 9t = 5[-3t + (9 * -3 + t * -3)] -15 + 9t = 5[-3t + (-27 + -3t)] Reorder the terms: -15 + 9t = 5[-27 + -3t + -3t] Combine like terms: -3t + -3t = -6t -15 + 9t = 5[-27 + -6t] -15 + 9t = [-27 * 5 + -6t * 5] -15 + 9t = [-135 + -30t] Solving -15 + 9t = -135 + -30t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '30t' to each side of the equation. -15 + 9t + 30t = -135 + -30t + 30t Combine like terms: 9t + 30t = 39t -15 + 39t = -135 + -30t + 30t Combine like terms: -30t + 30t = 0 -15 + 39t = -135 + 0 -15 + 39t = -135 Add '15' to each side of the equation. -15 + 15 + 39t = -135 + 15 Combine like terms: -15 + 15 = 0 0 + 39t = -135 + 15 39t = -135 + 15 Combine like terms: -135 + 15 = -120 39t = -120 Divide each side by '39'. t = -3.076923077 Simplifying t = -3.076923077
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