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Simplifying 4(a + 2b + -6) + 5(2a + 6b + -8) = 0 Reorder the terms: 4(-6 + a + 2b) + 5(2a + 6b + -8) = 0 (-6 * 4 + a * 4 + 2b * 4) + 5(2a + 6b + -8) = 0 (-24 + 4a + 8b) + 5(2a + 6b + -8) = 0 Reorder the terms: -24 + 4a + 8b + 5(-8 + 2a + 6b) = 0 -24 + 4a + 8b + (-8 * 5 + 2a * 5 + 6b * 5) = 0 -24 + 4a + 8b + (-40 + 10a + 30b) = 0 Reorder the terms: -24 + -40 + 4a + 10a + 8b + 30b = 0 Combine like terms: -24 + -40 = -64 -64 + 4a + 10a + 8b + 30b = 0 Combine like terms: 4a + 10a = 14a -64 + 14a + 8b + 30b = 0 Combine like terms: 8b + 30b = 38b -64 + 14a + 38b = 0 Solving -64 + 14a + 38b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '64' to each side of the equation. -64 + 14a + 64 + 38b = 0 + 64 Reorder the terms: -64 + 64 + 14a + 38b = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 14a + 38b = 0 + 64 14a + 38b = 0 + 64 Combine like terms: 0 + 64 = 64 14a + 38b = 64 Add '-38b' to each side of the equation. 14a + 38b + -38b = 64 + -38b Combine like terms: 38b + -38b = 0 14a + 0 = 64 + -38b 14a = 64 + -38b Divide each side by '14'. a = 4.571428571 + -2.714285714b Simplifying a = 4.571428571 + -2.714285714b
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