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Simplifying (15b + 3c + -15a) + -1(5a + -40c + 20b) = 0 Reorder the terms: (-15a + 15b + 3c) + -1(5a + -40c + 20b) = 0 Remove parenthesis around (-15a + 15b + 3c) -15a + 15b + 3c + -1(5a + -40c + 20b) = 0 Reorder the terms: -15a + 15b + 3c + -1(5a + 20b + -40c) = 0 -15a + 15b + 3c + (5a * -1 + 20b * -1 + -40c * -1) = 0 -15a + 15b + 3c + (-5a + -20b + 40c) = 0 Reorder the terms: -15a + -5a + 15b + -20b + 3c + 40c = 0 Combine like terms: -15a + -5a = -20a -20a + 15b + -20b + 3c + 40c = 0 Combine like terms: 15b + -20b = -5b -20a + -5b + 3c + 40c = 0 Combine like terms: 3c + 40c = 43c -20a + -5b + 43c = 0 Solving -20a + -5b + 43c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5b' to each side of the equation. -20a + -5b + 5b + 43c = 0 + 5b Combine like terms: -5b + 5b = 0 -20a + 0 + 43c = 0 + 5b -20a + 43c = 0 + 5b Remove the zero: -20a + 43c = 5b Add '-43c' to each side of the equation. -20a + 43c + -43c = 5b + -43c Combine like terms: 43c + -43c = 0 -20a + 0 = 5b + -43c -20a = 5b + -43c Divide each side by '-20'. a = -0.25b + 2.15c Simplifying a = -0.25b + 2.15c
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