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Simplifying 12(3a + 2b) + -8(5a + 4) = 0 (3a * 12 + 2b * 12) + -8(5a + 4) = 0 (36a + 24b) + -8(5a + 4) = 0 Reorder the terms: 36a + 24b + -8(4 + 5a) = 0 36a + 24b + (4 * -8 + 5a * -8) = 0 36a + 24b + (-32 + -40a) = 0 Reorder the terms: -32 + 36a + -40a + 24b = 0 Combine like terms: 36a + -40a = -4a -32 + -4a + 24b = 0 Solving -32 + -4a + 24b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '32' to each side of the equation. -32 + -4a + 32 + 24b = 0 + 32 Reorder the terms: -32 + 32 + -4a + 24b = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -4a + 24b = 0 + 32 -4a + 24b = 0 + 32 Combine like terms: 0 + 32 = 32 -4a + 24b = 32 Add '-24b' to each side of the equation. -4a + 24b + -24b = 32 + -24b Combine like terms: 24b + -24b = 0 -4a + 0 = 32 + -24b -4a = 32 + -24b Divide each side by '-4'. a = -8 + 6b Simplifying a = -8 + 6b
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