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Simplifying 12(4a + 5b) + -7(9a + 4b) = 0 (4a * 12 + 5b * 12) + -7(9a + 4b) = 0 (48a + 60b) + -7(9a + 4b) = 0 48a + 60b + (9a * -7 + 4b * -7) = 0 48a + 60b + (-63a + -28b) = 0 Reorder the terms: 48a + -63a + 60b + -28b = 0 Combine like terms: 48a + -63a = -15a -15a + 60b + -28b = 0 Combine like terms: 60b + -28b = 32b -15a + 32b = 0 Solving -15a + 32b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-32b' to each side of the equation. -15a + 32b + -32b = 0 + -32b Combine like terms: 32b + -32b = 0 -15a + 0 = 0 + -32b -15a = 0 + -32b Remove the zero: -15a = -32b Divide each side by '-15'. a = 2.133333333b Simplifying a = 2.133333333b
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