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Simplifying (ex + 1)(2x + 3)(x + 2) * x = 63 Reorder the terms: (1 + ex)(2x + 3)(x + 2) * x = 63 Reorder the terms: (1 + ex)(3 + 2x)(x + 2) * x = 63 Reorder the terms: (1 + ex)(3 + 2x)(2 + x) * x = 63 Reorder the terms for easier multiplication: x(1 + ex)(3 + 2x)(2 + x) = 63 Multiply (1 + ex) * (3 + 2x) x(1(3 + 2x) + ex(3 + 2x))(2 + x) = 63 x((3 * 1 + 2x * 1) + ex(3 + 2x))(2 + x) = 63 x((3 + 2x) + ex(3 + 2x))(2 + x) = 63 x(3 + 2x + (3 * ex + 2x * ex))(2 + x) = 63 x(3 + 2x + (3ex + 2ex2))(2 + x) = 63 Reorder the terms: x(3 + 3ex + 2ex2 + 2x)(2 + x) = 63 x(3 + 3ex + 2ex2 + 2x)(2 + x) = 63 Multiply (3 + 3ex + 2ex2 + 2x) * (2 + x) x(3(2 + x) + 3ex * (2 + x) + 2ex2 * (2 + x) + 2x * (2 + x)) = 63 x((2 * 3 + x * 3) + 3ex * (2 + x) + 2ex2 * (2 + x) + 2x * (2 + x)) = 63 x((6 + 3x) + 3ex * (2 + x) + 2ex2 * (2 + x) + 2x * (2 + x)) = 63 x(6 + 3x + (2 * 3ex + x * 3ex) + 2ex2 * (2 + x) + 2x * (2 + x)) = 63 x(6 + 3x + (6ex + 3ex2) + 2ex2 * (2 + x) + 2x * (2 + x)) = 63 x(6 + 3x + 6ex + 3ex2 + (2 * 2ex2 + x * 2ex2) + 2x * (2 + x)) = 63 x(6 + 3x + 6ex + 3ex2 + (4ex2 + 2ex3) + 2x * (2 + x)) = 63 x(6 + 3x + 6ex + 3ex2 + 4ex2 + 2ex3 + (2 * 2x + x * 2x)) = 63 x(6 + 3x + 6ex + 3ex2 + 4ex2 + 2ex3 + (4x + 2x2)) = 63 Reorder the terms: x(6 + 6ex + 3ex2 + 4ex2 + 2ex3 + 3x + 4x + 2x2) = 63 Combine like terms: 3ex2 + 4ex2 = 7ex2 x(6 + 6ex + 7ex2 + 2ex3 + 3x + 4x + 2x2) = 63 Combine like terms: 3x + 4x = 7x x(6 + 6ex + 7ex2 + 2ex3 + 7x + 2x2) = 63 (6 * x + 6ex * x + 7ex2 * x + 2ex3 * x + 7x * x + 2x2 * x) = 63 Reorder the terms: (6ex2 + 7ex3 + 2ex4 + 6x + 7x2 + 2x3) = 63 (6ex2 + 7ex3 + 2ex4 + 6x + 7x2 + 2x3) = 63 Solving 6ex2 + 7ex3 + 2ex4 + 6x + 7x2 + 2x3 = 63 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-6x' to each side of the equation. 6ex2 + 7ex3 + 2ex4 + 6x + 7x2 + -6x + 2x3 = 63 + -6x Reorder the terms: 6ex2 + 7ex3 + 2ex4 + 6x + -6x + 7x2 + 2x3 = 63 + -6x Combine like terms: 6x + -6x = 0 6ex2 + 7ex3 + 2ex4 + 0 + 7x2 + 2x3 = 63 + -6x 6ex2 + 7ex3 + 2ex4 + 7x2 + 2x3 = 63 + -6x Add '-7x2' to each side of the equation. 6ex2 + 7ex3 + 2ex4 + 7x2 + -7x2 + 2x3 = 63 + -6x + -7x2 Combine like terms: 7x2 + -7x2 = 0 6ex2 + 7ex3 + 2ex4 + 0 + 2x3 = 63 + -6x + -7x2 6ex2 + 7ex3 + 2ex4 + 2x3 = 63 + -6x + -7x2 Add '-2x3' to each side of the equation. 6ex2 + 7ex3 + 2ex4 + 2x3 + -2x3 = 63 + -6x + -7x2 + -2x3 Combine like terms: 2x3 + -2x3 = 0 6ex2 + 7ex3 + 2ex4 + 0 = 63 + -6x + -7x2 + -2x3 6ex2 + 7ex3 + 2ex4 = 63 + -6x + -7x2 + -2x3 Reorder the terms: -63 + 6ex2 + 7ex3 + 2ex4 + 6x + 7x2 + 2x3 = 63 + -6x + -7x2 + -2x3 + -63 + 6x + 7x2 + 2x3 Reorder the terms: -63 + 6ex2 + 7ex3 + 2ex4 + 6x + 7x2 + 2x3 = 63 + -63 + -6x + 6x + -7x2 + 7x2 + -2x3 + 2x3 Combine like terms: 63 + -63 = 0 -63 + 6ex2 + 7ex3 + 2ex4 + 6x + 7x2 + 2x3 = 0 + -6x + 6x + -7x2 + 7x2 + -2x3 + 2x3 -63 + 6ex2 + 7ex3 + 2ex4 + 6x + 7x2 + 2x3 = -6x + 6x + -7x2 + 7x2 + -2x3 + 2x3 Combine like terms: -6x + 6x = 0 -63 + 6ex2 + 7ex3 + 2ex4 + 6x + 7x2 + 2x3 = 0 + -7x2 + 7x2 + -2x3 + 2x3 -63 + 6ex2 + 7ex3 + 2ex4 + 6x + 7x2 + 2x3 = -7x2 + 7x2 + -2x3 + 2x3 Combine like terms: -7x2 + 7x2 = 0 -63 + 6ex2 + 7ex3 + 2ex4 + 6x + 7x2 + 2x3 = 0 + -2x3 + 2x3 -63 + 6ex2 + 7ex3 + 2ex4 + 6x + 7x2 + 2x3 = -2x3 + 2x3 Combine like terms: -2x3 + 2x3 = 0 -63 + 6ex2 + 7ex3 + 2ex4 + 6x + 7x2 + 2x3 = 0 The solution to this equation could not be determined.
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