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Simplifying 14 + -7t + 3(t + -2)(t + 2) = 2(1 + -1t)(1 + -1t) + t(t + -3) Reorder the terms: 14 + -7t + 3(-2 + t)(t + 2) = 2(1 + -1t)(1 + -1t) + t(t + -3) Reorder the terms: 14 + -7t + 3(-2 + t)(2 + t) = 2(1 + -1t)(1 + -1t) + t(t + -3) Multiply (-2 + t) * (2 + t) 14 + -7t + 3(-2(2 + t) + t(2 + t)) = 2(1 + -1t)(1 + -1t) + t(t + -3) 14 + -7t + 3((2 * -2 + t * -2) + t(2 + t)) = 2(1 + -1t)(1 + -1t) + t(t + -3) 14 + -7t + 3((-4 + -2t) + t(2 + t)) = 2(1 + -1t)(1 + -1t) + t(t + -3) 14 + -7t + 3(-4 + -2t + (2 * t + t * t)) = 2(1 + -1t)(1 + -1t) + t(t + -3) 14 + -7t + 3(-4 + -2t + (2t + t2)) = 2(1 + -1t)(1 + -1t) + t(t + -3) Combine like terms: -2t + 2t = 0 14 + -7t + 3(-4 + 0 + t2) = 2(1 + -1t)(1 + -1t) + t(t + -3) 14 + -7t + 3(-4 + t2) = 2(1 + -1t)(1 + -1t) + t(t + -3) 14 + -7t + (-4 * 3 + t2 * 3) = 2(1 + -1t)(1 + -1t) + t(t + -3) 14 + -7t + (-12 + 3t2) = 2(1 + -1t)(1 + -1t) + t(t + -3) Reorder the terms: 14 + -12 + -7t + 3t2 = 2(1 + -1t)(1 + -1t) + t(t + -3) Combine like terms: 14 + -12 = 2 2 + -7t + 3t2 = 2(1 + -1t)(1 + -1t) + t(t + -3) Multiply (1 + -1t) * (1 + -1t) 2 + -7t + 3t2 = 2(1(1 + -1t) + -1t * (1 + -1t)) + t(t + -3) 2 + -7t + 3t2 = 2((1 * 1 + -1t * 1) + -1t * (1 + -1t)) + t(t + -3) 2 + -7t + 3t2 = 2((1 + -1t) + -1t * (1 + -1t)) + t(t + -3) 2 + -7t + 3t2 = 2(1 + -1t + (1 * -1t + -1t * -1t)) + t(t + -3) 2 + -7t + 3t2 = 2(1 + -1t + (-1t + 1t2)) + t(t + -3) Combine like terms: -1t + -1t = -2t 2 + -7t + 3t2 = 2(1 + -2t + 1t2) + t(t + -3) 2 + -7t + 3t2 = (1 * 2 + -2t * 2 + 1t2 * 2) + t(t + -3) 2 + -7t + 3t2 = (2 + -4t + 2t2) + t(t + -3) Reorder the terms: 2 + -7t + 3t2 = 2 + -4t + 2t2 + t(-3 + t) 2 + -7t + 3t2 = 2 + -4t + 2t2 + (-3 * t + t * t) 2 + -7t + 3t2 = 2 + -4t + 2t2 + (-3t + t2) Reorder the terms: 2 + -7t + 3t2 = 2 + -4t + -3t + 2t2 + t2 Combine like terms: -4t + -3t = -7t 2 + -7t + 3t2 = 2 + -7t + 2t2 + t2 Combine like terms: 2t2 + t2 = 3t2 2 + -7t + 3t2 = 2 + -7t + 3t2 Add '-2' to each side of the equation. 2 + -7t + -2 + 3t2 = 2 + -7t + -2 + 3t2 Reorder the terms: 2 + -2 + -7t + 3t2 = 2 + -7t + -2 + 3t2 Combine like terms: 2 + -2 = 0 0 + -7t + 3t2 = 2 + -7t + -2 + 3t2 -7t + 3t2 = 2 + -7t + -2 + 3t2 Reorder the terms: -7t + 3t2 = 2 + -2 + -7t + 3t2 Combine like terms: 2 + -2 = 0 -7t + 3t2 = 0 + -7t + 3t2 -7t + 3t2 = -7t + 3t2 Add '7t' to each side of the equation. -7t + 7t + 3t2 = -7t + 7t + 3t2 Combine like terms: -7t + 7t = 0 0 + 3t2 = -7t + 7t + 3t2 3t2 = -7t + 7t + 3t2 Combine like terms: -7t + 7t = 0 3t2 = 0 + 3t2 3t2 = 3t2 Add '-3t2' to each side of the equation. 3t2 + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 0 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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