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Simplifying -7r2d + -5rd2 + 5rd + -1(-12r2d + -13rd2 + -7rd) = 0 Reorder the terms: -7dr2 + -5d2r + 5dr + -1(-7dr + -12dr2 + -13d2r) = 0 -7dr2 + -5d2r + 5dr + (-7dr * -1 + -12dr2 * -1 + -13d2r * -1) = 0 -7dr2 + -5d2r + 5dr + (7dr + 12dr2 + 13d2r) = 0 Reorder the terms: 5dr + 7dr + -7dr2 + 12dr2 + -5d2r + 13d2r = 0 Combine like terms: 5dr + 7dr = 12dr 12dr + -7dr2 + 12dr2 + -5d2r + 13d2r = 0 Combine like terms: -7dr2 + 12dr2 = 5dr2 12dr + 5dr2 + -5d2r + 13d2r = 0 Combine like terms: -5d2r + 13d2r = 8d2r 12dr + 5dr2 + 8d2r = 0 Solving 12dr + 5dr2 + 8d2r = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), 'dr'. dr(12 + 5r + 8d) = 0Subproblem 1
Set the factor 'dr' equal to zero and attempt to solve: Simplifying dr = 0 Solving dr = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dr = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(12 + 5r + 8d)' equal to zero and attempt to solve: Simplifying 12 + 5r + 8d = 0 Reorder the terms: 12 + 8d + 5r = 0 Solving 12 + 8d + 5r = 0 Move all terms containing d to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 8d + -12 + 5r = 0 + -12 Reorder the terms: 12 + -12 + 8d + 5r = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 8d + 5r = 0 + -12 8d + 5r = 0 + -12 Combine like terms: 0 + -12 = -12 8d + 5r = -12 Add '-5r' to each side of the equation. 8d + 5r + -5r = -12 + -5r Combine like terms: 5r + -5r = 0 8d + 0 = -12 + -5r 8d = -12 + -5r Divide each side by '8'. d = -1.5 + -0.625r Simplifying d = -1.5 + -0.625rSolution
d = {-1.5 + -0.625r}
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