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Simplifying 10(-4a + 3b + -4c) + -8(3a + -5b + 3c) = 0 (-4a * 10 + 3b * 10 + -4c * 10) + -8(3a + -5b + 3c) = 0 (-40a + 30b + -40c) + -8(3a + -5b + 3c) = 0 -40a + 30b + -40c + (3a * -8 + -5b * -8 + 3c * -8) = 0 -40a + 30b + -40c + (-24a + 40b + -24c) = 0 Reorder the terms: -40a + -24a + 30b + 40b + -40c + -24c = 0 Combine like terms: -40a + -24a = -64a -64a + 30b + 40b + -40c + -24c = 0 Combine like terms: 30b + 40b = 70b -64a + 70b + -40c + -24c = 0 Combine like terms: -40c + -24c = -64c -64a + 70b + -64c = 0 Solving -64a + 70b + -64c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-70b' to each side of the equation. -64a + 70b + -70b + -64c = 0 + -70b Combine like terms: 70b + -70b = 0 -64a + 0 + -64c = 0 + -70b -64a + -64c = 0 + -70b Remove the zero: -64a + -64c = -70b Add '64c' to each side of the equation. -64a + -64c + 64c = -70b + 64c Combine like terms: -64c + 64c = 0 -64a + 0 = -70b + 64c -64a = -70b + 64c Divide each side by '-64'. a = 1.09375b + -1c Simplifying a = 1.09375b + -1c
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