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Simplifying 3(2a + 5b) + -2(4a + -2b) = 0 (2a * 3 + 5b * 3) + -2(4a + -2b) = 0 (6a + 15b) + -2(4a + -2b) = 0 6a + 15b + (4a * -2 + -2b * -2) = 0 6a + 15b + (-8a + 4b) = 0 Reorder the terms: 6a + -8a + 15b + 4b = 0 Combine like terms: 6a + -8a = -2a -2a + 15b + 4b = 0 Combine like terms: 15b + 4b = 19b -2a + 19b = 0 Solving -2a + 19b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-19b' to each side of the equation. -2a + 19b + -19b = 0 + -19b Combine like terms: 19b + -19b = 0 -2a + 0 = 0 + -19b -2a = 0 + -19b Remove the zero: -2a = -19b Divide each side by '-2'. a = 9.5b Simplifying a = 9.5b
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