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Simplifying 3(2a + -1) = 5(4a + -1) + -4(3a + -2) Reorder the terms: 3(-1 + 2a) = 5(4a + -1) + -4(3a + -2) (-1 * 3 + 2a * 3) = 5(4a + -1) + -4(3a + -2) (-3 + 6a) = 5(4a + -1) + -4(3a + -2) Reorder the terms: -3 + 6a = 5(-1 + 4a) + -4(3a + -2) -3 + 6a = (-1 * 5 + 4a * 5) + -4(3a + -2) -3 + 6a = (-5 + 20a) + -4(3a + -2) Reorder the terms: -3 + 6a = -5 + 20a + -4(-2 + 3a) -3 + 6a = -5 + 20a + (-2 * -4 + 3a * -4) -3 + 6a = -5 + 20a + (8 + -12a) Reorder the terms: -3 + 6a = -5 + 8 + 20a + -12a Combine like terms: -5 + 8 = 3 -3 + 6a = 3 + 20a + -12a Combine like terms: 20a + -12a = 8a -3 + 6a = 3 + 8a Solving -3 + 6a = 3 + 8a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8a' to each side of the equation. -3 + 6a + -8a = 3 + 8a + -8a Combine like terms: 6a + -8a = -2a -3 + -2a = 3 + 8a + -8a Combine like terms: 8a + -8a = 0 -3 + -2a = 3 + 0 -3 + -2a = 3 Add '3' to each side of the equation. -3 + 3 + -2a = 3 + 3 Combine like terms: -3 + 3 = 0 0 + -2a = 3 + 3 -2a = 3 + 3 Combine like terms: 3 + 3 = 6 -2a = 6 Divide each side by '-2'. a = -3 Simplifying a = -3
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