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Simplifying 5(5a + -7b + 6) + 4(3a + -4b) = 0 Reorder the terms: 5(6 + 5a + -7b) + 4(3a + -4b) = 0 (6 * 5 + 5a * 5 + -7b * 5) + 4(3a + -4b) = 0 (30 + 25a + -35b) + 4(3a + -4b) = 0 30 + 25a + -35b + (3a * 4 + -4b * 4) = 0 30 + 25a + -35b + (12a + -16b) = 0 Reorder the terms: 30 + 25a + 12a + -35b + -16b = 0 Combine like terms: 25a + 12a = 37a 30 + 37a + -35b + -16b = 0 Combine like terms: -35b + -16b = -51b 30 + 37a + -51b = 0 Solving 30 + 37a + -51b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + 37a + -30 + -51b = 0 + -30 Reorder the terms: 30 + -30 + 37a + -51b = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 37a + -51b = 0 + -30 37a + -51b = 0 + -30 Combine like terms: 0 + -30 = -30 37a + -51b = -30 Add '51b' to each side of the equation. 37a + -51b + 51b = -30 + 51b Combine like terms: -51b + 51b = 0 37a + 0 = -30 + 51b 37a = -30 + 51b Divide each side by '37'. a = -0.8108108108 + 1.378378378b Simplifying a = -0.8108108108 + 1.378378378b
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