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Simplifying (4t + 1)(2t + -7) = (4t + -3)(2t + 7) Reorder the terms: (1 + 4t)(2t + -7) = (4t + -3)(2t + 7) Reorder the terms: (1 + 4t)(-7 + 2t) = (4t + -3)(2t + 7) Multiply (1 + 4t) * (-7 + 2t) (1(-7 + 2t) + 4t * (-7 + 2t)) = (4t + -3)(2t + 7) ((-7 * 1 + 2t * 1) + 4t * (-7 + 2t)) = (4t + -3)(2t + 7) ((-7 + 2t) + 4t * (-7 + 2t)) = (4t + -3)(2t + 7) (-7 + 2t + (-7 * 4t + 2t * 4t)) = (4t + -3)(2t + 7) (-7 + 2t + (-28t + 8t2)) = (4t + -3)(2t + 7) Combine like terms: 2t + -28t = -26t (-7 + -26t + 8t2) = (4t + -3)(2t + 7) Reorder the terms: -7 + -26t + 8t2 = (-3 + 4t)(2t + 7) Reorder the terms: -7 + -26t + 8t2 = (-3 + 4t)(7 + 2t) Multiply (-3 + 4t) * (7 + 2t) -7 + -26t + 8t2 = (-3(7 + 2t) + 4t * (7 + 2t)) -7 + -26t + 8t2 = ((7 * -3 + 2t * -3) + 4t * (7 + 2t)) -7 + -26t + 8t2 = ((-21 + -6t) + 4t * (7 + 2t)) -7 + -26t + 8t2 = (-21 + -6t + (7 * 4t + 2t * 4t)) -7 + -26t + 8t2 = (-21 + -6t + (28t + 8t2)) Combine like terms: -6t + 28t = 22t -7 + -26t + 8t2 = (-21 + 22t + 8t2) Add '-8t2' to each side of the equation. -7 + -26t + 8t2 + -8t2 = -21 + 22t + 8t2 + -8t2 Combine like terms: 8t2 + -8t2 = 0 -7 + -26t + 0 = -21 + 22t + 8t2 + -8t2 -7 + -26t = -21 + 22t + 8t2 + -8t2 Combine like terms: 8t2 + -8t2 = 0 -7 + -26t = -21 + 22t + 0 -7 + -26t = -21 + 22t Solving -7 + -26t = -21 + 22t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-22t' to each side of the equation. -7 + -26t + -22t = -21 + 22t + -22t Combine like terms: -26t + -22t = -48t -7 + -48t = -21 + 22t + -22t Combine like terms: 22t + -22t = 0 -7 + -48t = -21 + 0 -7 + -48t = -21 Add '7' to each side of the equation. -7 + 7 + -48t = -21 + 7 Combine like terms: -7 + 7 = 0 0 + -48t = -21 + 7 -48t = -21 + 7 Combine like terms: -21 + 7 = -14 -48t = -14 Divide each side by '-48'. t = 0.2916666667 Simplifying t = 0.2916666667
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