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Simplifying 4(5b + c + -5a) + -5(a + -6c + 6b) = 0 Reorder the terms: 4(-5a + 5b + c) + -5(a + -6c + 6b) = 0 (-5a * 4 + 5b * 4 + c * 4) + -5(a + -6c + 6b) = 0 (-20a + 20b + 4c) + -5(a + -6c + 6b) = 0 Reorder the terms: -20a + 20b + 4c + -5(a + 6b + -6c) = 0 -20a + 20b + 4c + (a * -5 + 6b * -5 + -6c * -5) = 0 -20a + 20b + 4c + (-5a + -30b + 30c) = 0 Reorder the terms: -20a + -5a + 20b + -30b + 4c + 30c = 0 Combine like terms: -20a + -5a = -25a -25a + 20b + -30b + 4c + 30c = 0 Combine like terms: 20b + -30b = -10b -25a + -10b + 4c + 30c = 0 Combine like terms: 4c + 30c = 34c -25a + -10b + 34c = 0 Solving -25a + -10b + 34c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10b' to each side of the equation. -25a + -10b + 10b + 34c = 0 + 10b Combine like terms: -10b + 10b = 0 -25a + 0 + 34c = 0 + 10b -25a + 34c = 0 + 10b Remove the zero: -25a + 34c = 10b Add '-34c' to each side of the equation. -25a + 34c + -34c = 10b + -34c Combine like terms: 34c + -34c = 0 -25a + 0 = 10b + -34c -25a = 10b + -34c Divide each side by '-25'. a = -0.4b + 1.36c Simplifying a = -0.4b + 1.36c
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