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Simplifying 45a3d + -75a2d2 + -30ad3 = 0 Reorder the terms: -30ad3 + -75a2d2 + 45a3d = 0 Solving -30ad3 + -75a2d2 + 45a3d = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '15ad'. 15ad(-2d2 + -5ad + 3a2) = 0 Factor a trinomial. 15ad((-1d + -3a)(2d + -1a)) = 0 Ignore the factor 15.Subproblem 1
Set the factor 'ad' equal to zero and attempt to solve: Simplifying ad = 0 Solving ad = 0 Move all terms containing a to the left, all other terms to the right. Simplifying ad = 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 '(-1d + -3a)' equal to zero and attempt to solve: Simplifying -1d + -3a = 0 Reorder the terms: -3a + -1d = 0 Solving -3a + -1d = 0 Move all terms containing a to the left, all other terms to the right. Add 'd' to each side of the equation. -3a + -1d + d = 0 + d Combine like terms: -1d + d = 0 -3a + 0 = 0 + d -3a = 0 + d Remove the zero: -3a = d Divide each side by '-3'. a = -0.3333333333d Simplifying a = -0.3333333333dSubproblem 3
Set the factor '(2d + -1a)' equal to zero and attempt to solve: Simplifying 2d + -1a = 0 Reorder the terms: -1a + 2d = 0 Solving -1a + 2d = 0 Move all terms containing a to the left, all other terms to the right. Add '-2d' to each side of the equation. -1a + 2d + -2d = 0 + -2d Combine like terms: 2d + -2d = 0 -1a + 0 = 0 + -2d -1a = 0 + -2d Remove the zero: -1a = -2d Divide each side by '-1'. a = 2d Simplifying a = 2dSolution
a = {-0.3333333333d, 2d}
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