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Simplifying (t + 2)(t + -2) = (t + 3)(t + -4) + 5 Reorder the terms: (2 + t)(t + -2) = (t + 3)(t + -4) + 5 Reorder the terms: (2 + t)(-2 + t) = (t + 3)(t + -4) + 5 Multiply (2 + t) * (-2 + t) (2(-2 + t) + t(-2 + t)) = (t + 3)(t + -4) + 5 ((-2 * 2 + t * 2) + t(-2 + t)) = (t + 3)(t + -4) + 5 ((-4 + 2t) + t(-2 + t)) = (t + 3)(t + -4) + 5 (-4 + 2t + (-2 * t + t * t)) = (t + 3)(t + -4) + 5 (-4 + 2t + (-2t + t2)) = (t + 3)(t + -4) + 5 Combine like terms: 2t + -2t = 0 (-4 + 0 + t2) = (t + 3)(t + -4) + 5 (-4 + t2) = (t + 3)(t + -4) + 5 Reorder the terms: -4 + t2 = (3 + t)(t + -4) + 5 Reorder the terms: -4 + t2 = (3 + t)(-4 + t) + 5 Multiply (3 + t) * (-4 + t) -4 + t2 = (3(-4 + t) + t(-4 + t)) + 5 -4 + t2 = ((-4 * 3 + t * 3) + t(-4 + t)) + 5 -4 + t2 = ((-12 + 3t) + t(-4 + t)) + 5 -4 + t2 = (-12 + 3t + (-4 * t + t * t)) + 5 -4 + t2 = (-12 + 3t + (-4t + t2)) + 5 Combine like terms: 3t + -4t = -1t -4 + t2 = (-12 + -1t + t2) + 5 Reorder the terms: -4 + t2 = -12 + 5 + -1t + t2 Combine like terms: -12 + 5 = -7 -4 + t2 = -7 + -1t + t2 Add '-1t2' to each side of the equation. -4 + t2 + -1t2 = -7 + -1t + t2 + -1t2 Combine like terms: t2 + -1t2 = 0 -4 + 0 = -7 + -1t + t2 + -1t2 -4 = -7 + -1t + t2 + -1t2 Combine like terms: t2 + -1t2 = 0 -4 = -7 + -1t + 0 -4 = -7 + -1t Solving -4 = -7 + -1t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add 't' to each side of the equation. -4 + t = -7 + -1t + t Combine like terms: -1t + t = 0 -4 + t = -7 + 0 -4 + t = -7 Add '4' to each side of the equation. -4 + 4 + t = -7 + 4 Combine like terms: -4 + 4 = 0 0 + t = -7 + 4 t = -7 + 4 Combine like terms: -7 + 4 = -3 t = -3 Simplifying t = -3
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