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Simplifying 12 + -2(-3d + 2f) + 7f + -11d + -21 = 0 12 + (-3d * -2 + 2f * -2) + 7f + -11d + -21 = 0 12 + (6d + -4f) + 7f + -11d + -21 = 0 Reorder the terms: 12 + -21 + 6d + -11d + -4f + 7f = 0 Combine like terms: 12 + -21 = -9 -9 + 6d + -11d + -4f + 7f = 0 Combine like terms: 6d + -11d = -5d -9 + -5d + -4f + 7f = 0 Combine like terms: -4f + 7f = 3f -9 + -5d + 3f = 0 Solving -9 + -5d + 3f = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '9' to each side of the equation. -9 + -5d + 9 + 3f = 0 + 9 Reorder the terms: -9 + 9 + -5d + 3f = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5d + 3f = 0 + 9 -5d + 3f = 0 + 9 Combine like terms: 0 + 9 = 9 -5d + 3f = 9 Add '-3f' to each side of the equation. -5d + 3f + -3f = 9 + -3f Combine like terms: 3f + -3f = 0 -5d + 0 = 9 + -3f -5d = 9 + -3f Divide each side by '-5'. d = -1.8 + 0.6f Simplifying d = -1.8 + 0.6f
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