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Simplifying 2(15a + -6b) + -1(-2a + 3b + -5) = 0 (15a * 2 + -6b * 2) + -1(-2a + 3b + -5) = 0 (30a + -12b) + -1(-2a + 3b + -5) = 0 Reorder the terms: 30a + -12b + -1(-5 + -2a + 3b) = 0 30a + -12b + (-5 * -1 + -2a * -1 + 3b * -1) = 0 30a + -12b + (5 + 2a + -3b) = 0 Reorder the terms: 5 + 30a + 2a + -12b + -3b = 0 Combine like terms: 30a + 2a = 32a 5 + 32a + -12b + -3b = 0 Combine like terms: -12b + -3b = -15b 5 + 32a + -15b = 0 Solving 5 + 32a + -15b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + 32a + -5 + -15b = 0 + -5 Reorder the terms: 5 + -5 + 32a + -15b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 32a + -15b = 0 + -5 32a + -15b = 0 + -5 Combine like terms: 0 + -5 = -5 32a + -15b = -5 Add '15b' to each side of the equation. 32a + -15b + 15b = -5 + 15b Combine like terms: -15b + 15b = 0 32a + 0 = -5 + 15b 32a = -5 + 15b Divide each side by '32'. a = -0.15625 + 0.46875b Simplifying a = -0.15625 + 0.46875b
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