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Simplifying -8a + -4b + 18a + -5c + 2c + -12d + e + -45d + 4c = 0 Reorder the terms: -8a + 18a + -4b + -5c + 2c + 4c + -12d + -45d + e = 0 Combine like terms: -8a + 18a = 10a 10a + -4b + -5c + 2c + 4c + -12d + -45d + e = 0 Combine like terms: -5c + 2c = -3c 10a + -4b + -3c + 4c + -12d + -45d + e = 0 Combine like terms: -3c + 4c = 1c 10a + -4b + 1c + -12d + -45d + e = 0 Combine like terms: -12d + -45d = -57d 10a + -4b + 1c + -57d + e = 0 Solving 10a + -4b + 1c + -57d + e = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4b' to each side of the equation. 10a + -4b + 1c + -57d + 4b + e = 0 + 4b Reorder the terms: 10a + -4b + 4b + 1c + -57d + e = 0 + 4b Combine like terms: -4b + 4b = 0 10a + 0 + 1c + -57d + e = 0 + 4b 10a + 1c + -57d + e = 0 + 4b Remove the zero: 10a + 1c + -57d + e = 4b Add '-1c' to each side of the equation. 10a + 1c + -57d + -1c + e = 4b + -1c Reorder the terms: 10a + 1c + -1c + -57d + e = 4b + -1c Combine like terms: 1c + -1c = 0 10a + 0 + -57d + e = 4b + -1c 10a + -57d + e = 4b + -1c Add '57d' to each side of the equation. 10a + -57d + 57d + e = 4b + -1c + 57d Combine like terms: -57d + 57d = 0 10a + 0 + e = 4b + -1c + 57d 10a + e = 4b + -1c + 57d Add '-1e' to each side of the equation. 10a + e + -1e = 4b + -1c + 57d + -1e Combine like terms: e + -1e = 0 10a + 0 = 4b + -1c + 57d + -1e 10a = 4b + -1c + 57d + -1e Divide each side by '10'. a = 0.4b + -0.1c + 5.7d + -0.1e Simplifying a = 0.4b + -0.1c + 5.7d + -0.1e
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