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Simplifying 5(3a + e) + -4(d + -4e) = 0 (3a * 5 + e * 5) + -4(d + -4e) = 0 (15a + 5e) + -4(d + -4e) = 0 15a + 5e + (d * -4 + -4e * -4) = 0 15a + 5e + (-4d + 16e) = 0 Reorder the terms: 15a + -4d + 5e + 16e = 0 Combine like terms: 5e + 16e = 21e 15a + -4d + 21e = 0 Solving 15a + -4d + 21e = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4d' to each side of the equation. 15a + -4d + 4d + 21e = 0 + 4d Combine like terms: -4d + 4d = 0 15a + 0 + 21e = 0 + 4d 15a + 21e = 0 + 4d Remove the zero: 15a + 21e = 4d Add '-21e' to each side of the equation. 15a + 21e + -21e = 4d + -21e Combine like terms: 21e + -21e = 0 15a + 0 = 4d + -21e 15a = 4d + -21e Divide each side by '15'. a = 0.2666666667d + -1.4e Simplifying a = 0.2666666667d + -1.4e
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