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Simplifying (6t + 7)(2t + -3) = (2t + 4)(6t + 5) Reorder the terms: (7 + 6t)(2t + -3) = (2t + 4)(6t + 5) Reorder the terms: (7 + 6t)(-3 + 2t) = (2t + 4)(6t + 5) Multiply (7 + 6t) * (-3 + 2t) (7(-3 + 2t) + 6t * (-3 + 2t)) = (2t + 4)(6t + 5) ((-3 * 7 + 2t * 7) + 6t * (-3 + 2t)) = (2t + 4)(6t + 5) ((-21 + 14t) + 6t * (-3 + 2t)) = (2t + 4)(6t + 5) (-21 + 14t + (-3 * 6t + 2t * 6t)) = (2t + 4)(6t + 5) (-21 + 14t + (-18t + 12t2)) = (2t + 4)(6t + 5) Combine like terms: 14t + -18t = -4t (-21 + -4t + 12t2) = (2t + 4)(6t + 5) Reorder the terms: -21 + -4t + 12t2 = (4 + 2t)(6t + 5) Reorder the terms: -21 + -4t + 12t2 = (4 + 2t)(5 + 6t) Multiply (4 + 2t) * (5 + 6t) -21 + -4t + 12t2 = (4(5 + 6t) + 2t * (5 + 6t)) -21 + -4t + 12t2 = ((5 * 4 + 6t * 4) + 2t * (5 + 6t)) -21 + -4t + 12t2 = ((20 + 24t) + 2t * (5 + 6t)) -21 + -4t + 12t2 = (20 + 24t + (5 * 2t + 6t * 2t)) -21 + -4t + 12t2 = (20 + 24t + (10t + 12t2)) Combine like terms: 24t + 10t = 34t -21 + -4t + 12t2 = (20 + 34t + 12t2) Add '-12t2' to each side of the equation. -21 + -4t + 12t2 + -12t2 = 20 + 34t + 12t2 + -12t2 Combine like terms: 12t2 + -12t2 = 0 -21 + -4t + 0 = 20 + 34t + 12t2 + -12t2 -21 + -4t = 20 + 34t + 12t2 + -12t2 Combine like terms: 12t2 + -12t2 = 0 -21 + -4t = 20 + 34t + 0 -21 + -4t = 20 + 34t Solving -21 + -4t = 20 + 34t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-34t' to each side of the equation. -21 + -4t + -34t = 20 + 34t + -34t Combine like terms: -4t + -34t = -38t -21 + -38t = 20 + 34t + -34t Combine like terms: 34t + -34t = 0 -21 + -38t = 20 + 0 -21 + -38t = 20 Add '21' to each side of the equation. -21 + 21 + -38t = 20 + 21 Combine like terms: -21 + 21 = 0 0 + -38t = 20 + 21 -38t = 20 + 21 Combine like terms: 20 + 21 = 41 -38t = 41 Divide each side by '-38'. t = -1.078947368 Simplifying t = -1.078947368
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