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Simplifying 2(2t + -6) = 3(4t + -9) Reorder the terms: 2(-6 + 2t) = 3(4t + -9) (-6 * 2 + 2t * 2) = 3(4t + -9) (-12 + 4t) = 3(4t + -9) Reorder the terms: -12 + 4t = 3(-9 + 4t) -12 + 4t = (-9 * 3 + 4t * 3) -12 + 4t = (-27 + 12t) Solving -12 + 4t = -27 + 12t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-12t' to each side of the equation. -12 + 4t + -12t = -27 + 12t + -12t Combine like terms: 4t + -12t = -8t -12 + -8t = -27 + 12t + -12t Combine like terms: 12t + -12t = 0 -12 + -8t = -27 + 0 -12 + -8t = -27 Add '12' to each side of the equation. -12 + 12 + -8t = -27 + 12 Combine like terms: -12 + 12 = 0 0 + -8t = -27 + 12 -8t = -27 + 12 Combine like terms: -27 + 12 = -15 -8t = -15 Divide each side by '-8'. t = 1.875 Simplifying t = 1.875
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