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Simplifying 5(4a + -1b) + -8(5b + -7a) = 0 (4a * 5 + -1b * 5) + -8(5b + -7a) = 0 (20a + -5b) + -8(5b + -7a) = 0 Reorder the terms: 20a + -5b + -8(-7a + 5b) = 0 20a + -5b + (-7a * -8 + 5b * -8) = 0 20a + -5b + (56a + -40b) = 0 Reorder the terms: 20a + 56a + -5b + -40b = 0 Combine like terms: 20a + 56a = 76a 76a + -5b + -40b = 0 Combine like terms: -5b + -40b = -45b 76a + -45b = 0 Solving 76a + -45b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '45b' to each side of the equation. 76a + -45b + 45b = 0 + 45b Combine like terms: -45b + 45b = 0 76a + 0 = 0 + 45b 76a = 0 + 45b Remove the zero: 76a = 45b Divide each side by '76'. a = 0.5921052632b Simplifying a = 0.5921052632b
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