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Simplifying 15(a + -1b) + -9(10b + -12a) = 0 (a * 15 + -1b * 15) + -9(10b + -12a) = 0 (15a + -15b) + -9(10b + -12a) = 0 Reorder the terms: 15a + -15b + -9(-12a + 10b) = 0 15a + -15b + (-12a * -9 + 10b * -9) = 0 15a + -15b + (108a + -90b) = 0 Reorder the terms: 15a + 108a + -15b + -90b = 0 Combine like terms: 15a + 108a = 123a 123a + -15b + -90b = 0 Combine like terms: -15b + -90b = -105b 123a + -105b = 0 Solving 123a + -105b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '105b' to each side of the equation. 123a + -105b + 105b = 0 + 105b Combine like terms: -105b + 105b = 0 123a + 0 = 0 + 105b 123a = 0 + 105b Remove the zero: 123a = 105b Divide each side by '123'. a = 0.8536585366b Simplifying a = 0.8536585366b
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