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Simplifying 6(5t + -1) + -6 = -3t + 3(3t + -8) Reorder the terms: 6(-1 + 5t) + -6 = -3t + 3(3t + -8) (-1 * 6 + 5t * 6) + -6 = -3t + 3(3t + -8) (-6 + 30t) + -6 = -3t + 3(3t + -8) Reorder the terms: -6 + -6 + 30t = -3t + 3(3t + -8) Combine like terms: -6 + -6 = -12 -12 + 30t = -3t + 3(3t + -8) Reorder the terms: -12 + 30t = -3t + 3(-8 + 3t) -12 + 30t = -3t + (-8 * 3 + 3t * 3) -12 + 30t = -3t + (-24 + 9t) Reorder the terms: -12 + 30t = -24 + -3t + 9t Combine like terms: -3t + 9t = 6t -12 + 30t = -24 + 6t Solving -12 + 30t = -24 + 6t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6t' to each side of the equation. -12 + 30t + -6t = -24 + 6t + -6t Combine like terms: 30t + -6t = 24t -12 + 24t = -24 + 6t + -6t Combine like terms: 6t + -6t = 0 -12 + 24t = -24 + 0 -12 + 24t = -24 Add '12' to each side of the equation. -12 + 12 + 24t = -24 + 12 Combine like terms: -12 + 12 = 0 0 + 24t = -24 + 12 24t = -24 + 12 Combine like terms: -24 + 12 = -12 24t = -12 Divide each side by '24'. t = -0.5 Simplifying t = -0.5
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