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Simplifying 4(a + -3) + -5(2a + -1b) + 3(b + 2) = 0 Reorder the terms: 4(-3 + a) + -5(2a + -1b) + 3(b + 2) = 0 (-3 * 4 + a * 4) + -5(2a + -1b) + 3(b + 2) = 0 (-12 + 4a) + -5(2a + -1b) + 3(b + 2) = 0 -12 + 4a + (2a * -5 + -1b * -5) + 3(b + 2) = 0 -12 + 4a + (-10a + 5b) + 3(b + 2) = 0 Reorder the terms: -12 + 4a + -10a + 5b + 3(2 + b) = 0 -12 + 4a + -10a + 5b + (2 * 3 + b * 3) = 0 -12 + 4a + -10a + 5b + (6 + 3b) = 0 Reorder the terms: -12 + 6 + 4a + -10a + 5b + 3b = 0 Combine like terms: -12 + 6 = -6 -6 + 4a + -10a + 5b + 3b = 0 Combine like terms: 4a + -10a = -6a -6 + -6a + 5b + 3b = 0 Combine like terms: 5b + 3b = 8b -6 + -6a + 8b = 0 Solving -6 + -6a + 8b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + -6a + 6 + 8b = 0 + 6 Reorder the terms: -6 + 6 + -6a + 8b = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -6a + 8b = 0 + 6 -6a + 8b = 0 + 6 Combine like terms: 0 + 6 = 6 -6a + 8b = 6 Add '-8b' to each side of the equation. -6a + 8b + -8b = 6 + -8b Combine like terms: 8b + -8b = 0 -6a + 0 = 6 + -8b -6a = 6 + -8b Divide each side by '-6'. a = -1 + 1.333333333b Simplifying a = -1 + 1.333333333b
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