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Simplifying 4(9b + c + -5a) + -5(a + -3c + 4b) = 0 Reorder the terms: 4(-5a + 9b + c) + -5(a + -3c + 4b) = 0 (-5a * 4 + 9b * 4 + c * 4) + -5(a + -3c + 4b) = 0 (-20a + 36b + 4c) + -5(a + -3c + 4b) = 0 Reorder the terms: -20a + 36b + 4c + -5(a + 4b + -3c) = 0 -20a + 36b + 4c + (a * -5 + 4b * -5 + -3c * -5) = 0 -20a + 36b + 4c + (-5a + -20b + 15c) = 0 Reorder the terms: -20a + -5a + 36b + -20b + 4c + 15c = 0 Combine like terms: -20a + -5a = -25a -25a + 36b + -20b + 4c + 15c = 0 Combine like terms: 36b + -20b = 16b -25a + 16b + 4c + 15c = 0 Combine like terms: 4c + 15c = 19c -25a + 16b + 19c = 0 Solving -25a + 16b + 19c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-16b' to each side of the equation. -25a + 16b + -16b + 19c = 0 + -16b Combine like terms: 16b + -16b = 0 -25a + 0 + 19c = 0 + -16b -25a + 19c = 0 + -16b Remove the zero: -25a + 19c = -16b Add '-19c' to each side of the equation. -25a + 19c + -19c = -16b + -19c Combine like terms: 19c + -19c = 0 -25a + 0 = -16b + -19c -25a = -16b + -19c Divide each side by '-25'. a = 0.64b + 0.76c Simplifying a = 0.64b + 0.76c
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