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Simplifying -5(2a + -3b) + 5(3b + -2a) = 0 (2a * -5 + -3b * -5) + 5(3b + -2a) = 0 (-10a + 15b) + 5(3b + -2a) = 0 Reorder the terms: -10a + 15b + 5(-2a + 3b) = 0 -10a + 15b + (-2a * 5 + 3b * 5) = 0 -10a + 15b + (-10a + 15b) = 0 Reorder the terms: -10a + -10a + 15b + 15b = 0 Combine like terms: -10a + -10a = -20a -20a + 15b + 15b = 0 Combine like terms: 15b + 15b = 30b -20a + 30b = 0 Solving -20a + 30b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-30b' to each side of the equation. -20a + 30b + -30b = 0 + -30b Combine like terms: 30b + -30b = 0 -20a + 0 = 0 + -30b -20a = 0 + -30b Remove the zero: -20a = -30b Divide each side by '-20'. a = 1.5b Simplifying a = 1.5b
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