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Simplifying 6[a + -3b + 5c] + -4[5b + -1c + 2a] = 0 [a * 6 + -3b * 6 + 5c * 6] + -4[5b + -1c + 2a] = 0 [6a + -18b + 30c] + -4[5b + -1c + 2a] = 0 Reorder the terms: 6a + -18b + 30c + -4[2a + 5b + -1c] = 0 6a + -18b + 30c + [2a * -4 + 5b * -4 + -1c * -4] = 0 6a + -18b + 30c + [-8a + -20b + 4c] = 0 Reorder the terms: 6a + -8a + -18b + -20b + 30c + 4c = 0 Combine like terms: 6a + -8a = -2a -2a + -18b + -20b + 30c + 4c = 0 Combine like terms: -18b + -20b = -38b -2a + -38b + 30c + 4c = 0 Combine like terms: 30c + 4c = 34c -2a + -38b + 34c = 0 Solving -2a + -38b + 34c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '38b' to each side of the equation. -2a + -38b + 38b + 34c = 0 + 38b Combine like terms: -38b + 38b = 0 -2a + 0 + 34c = 0 + 38b -2a + 34c = 0 + 38b Remove the zero: -2a + 34c = 38b Add '-34c' to each side of the equation. -2a + 34c + -34c = 38b + -34c Combine like terms: 34c + -34c = 0 -2a + 0 = 38b + -34c -2a = 38b + -34c Divide each side by '-2'. a = -19b + 17c Simplifying a = -19b + 17c
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