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Simplifying 13(4a + 5b) + -7(8a + 3) = 0 (4a * 13 + 5b * 13) + -7(8a + 3) = 0 (52a + 65b) + -7(8a + 3) = 0 Reorder the terms: 52a + 65b + -7(3 + 8a) = 0 52a + 65b + (3 * -7 + 8a * -7) = 0 52a + 65b + (-21 + -56a) = 0 Reorder the terms: -21 + 52a + -56a + 65b = 0 Combine like terms: 52a + -56a = -4a -21 + -4a + 65b = 0 Solving -21 + -4a + 65b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '21' to each side of the equation. -21 + -4a + 21 + 65b = 0 + 21 Reorder the terms: -21 + 21 + -4a + 65b = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -4a + 65b = 0 + 21 -4a + 65b = 0 + 21 Combine like terms: 0 + 21 = 21 -4a + 65b = 21 Add '-65b' to each side of the equation. -4a + 65b + -65b = 21 + -65b Combine like terms: 65b + -65b = 0 -4a + 0 = 21 + -65b -4a = 21 + -65b Divide each side by '-4'. a = -5.25 + 16.25b Simplifying a = -5.25 + 16.25b
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