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Simplifying 12x(a + -1b) + (c + d) * 3 = 0 (a * 12x + -1b * 12x) + (c + d) * 3 = 0 (12ax + -12bx) + (c + d) * 3 = 0 Reorder the terms for easier multiplication: 12ax + -12bx + 3(c + d) = 0 12ax + -12bx + (c * 3 + d * 3) = 0 12ax + -12bx + (3c + 3d) = 0 Solving 12ax + -12bx + 3c + 3d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12bx' to each side of the equation. 12ax + -12bx + 3c + 12bx + 3d = 0 + 12bx Reorder the terms: 12ax + -12bx + 12bx + 3c + 3d = 0 + 12bx Combine like terms: -12bx + 12bx = 0 12ax + 0 + 3c + 3d = 0 + 12bx 12ax + 3c + 3d = 0 + 12bx Remove the zero: 12ax + 3c + 3d = 12bx Add '-3c' to each side of the equation. 12ax + 3c + -3c + 3d = 12bx + -3c Combine like terms: 3c + -3c = 0 12ax + 0 + 3d = 12bx + -3c 12ax + 3d = 12bx + -3c Add '-3d' to each side of the equation. 12ax + 3d + -3d = 12bx + -3c + -3d Combine like terms: 3d + -3d = 0 12ax + 0 = 12bx + -3c + -3d 12ax = 12bx + -3c + -3d Divide each side by '12x'. a = b + -0.25cx-1 + -0.25dx-1 Simplifying a = b + -0.25cx-1 + -0.25dx-1
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