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Simplifying (4a + -3b + c + -5d) * 5 = 0 Reorder the terms for easier multiplication: 5(4a + -3b + c + -5d) = 0 (4a * 5 + -3b * 5 + c * 5 + -5d * 5) = 0 (20a + -15b + 5c + -25d) = 0 Solving 20a + -15b + 5c + -25d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '15b' to each side of the equation. 20a + -15b + 5c + 15b + -25d = 0 + 15b Reorder the terms: 20a + -15b + 15b + 5c + -25d = 0 + 15b Combine like terms: -15b + 15b = 0 20a + 0 + 5c + -25d = 0 + 15b 20a + 5c + -25d = 0 + 15b Remove the zero: 20a + 5c + -25d = 15b Add '-5c' to each side of the equation. 20a + 5c + -5c + -25d = 15b + -5c Combine like terms: 5c + -5c = 0 20a + 0 + -25d = 15b + -5c 20a + -25d = 15b + -5c Add '25d' to each side of the equation. 20a + -25d + 25d = 15b + -5c + 25d Combine like terms: -25d + 25d = 0 20a + 0 = 15b + -5c + 25d 20a = 15b + -5c + 25d Divide each side by '20'. a = 0.75b + -0.25c + 1.25d Simplifying a = 0.75b + -0.25c + 1.25d
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