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Simplifying 3(a + -4) = 5(2a + 3) + -2(3a + -5) Reorder the terms: 3(-4 + a) = 5(2a + 3) + -2(3a + -5) (-4 * 3 + a * 3) = 5(2a + 3) + -2(3a + -5) (-12 + 3a) = 5(2a + 3) + -2(3a + -5) Reorder the terms: -12 + 3a = 5(3 + 2a) + -2(3a + -5) -12 + 3a = (3 * 5 + 2a * 5) + -2(3a + -5) -12 + 3a = (15 + 10a) + -2(3a + -5) Reorder the terms: -12 + 3a = 15 + 10a + -2(-5 + 3a) -12 + 3a = 15 + 10a + (-5 * -2 + 3a * -2) -12 + 3a = 15 + 10a + (10 + -6a) Reorder the terms: -12 + 3a = 15 + 10 + 10a + -6a Combine like terms: 15 + 10 = 25 -12 + 3a = 25 + 10a + -6a Combine like terms: 10a + -6a = 4a -12 + 3a = 25 + 4a Solving -12 + 3a = 25 + 4a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4a' to each side of the equation. -12 + 3a + -4a = 25 + 4a + -4a Combine like terms: 3a + -4a = -1a -12 + -1a = 25 + 4a + -4a Combine like terms: 4a + -4a = 0 -12 + -1a = 25 + 0 -12 + -1a = 25 Add '12' to each side of the equation. -12 + 12 + -1a = 25 + 12 Combine like terms: -12 + 12 = 0 0 + -1a = 25 + 12 -1a = 25 + 12 Combine like terms: 25 + 12 = 37 -1a = 37 Divide each side by '-1'. a = -37 Simplifying a = -37
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