32a^3-24a^2+36a=0

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Solution for 32a^3-24a^2+36a=0 equation: 


Simplifying
32a3 + -24a2 + 36a = 0

Reorder the terms:
36a + -24a2 + 32a3 = 0

Solving
36a + -24a2 + 32a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a'.
4a(9 + -6a + 8a2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

Move all terms containing a to the left, all other terms to the right.

Simplifying
a = 0

Subproblem 2
Set the factor '(9 + -6a + 8a2)' equal to zero and attempt to solve:

Simplifying
9 + -6a + 8a2 = 0

Solving
9 + -6a + 8a2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
1.125 + -0.75a + a2 = 0

Move the constant term to the right:

Add '-1.125' to each side of the equation.
1.125 + -0.75a + -1.125 + a2 = 0 + -1.125

Reorder the terms:
1.125 + -1.125 + -0.75a + a2 = 0 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + -0.75a + a2 = 0 + -1.125
-0.75a + a2 = 0 + -1.125

Combine like terms: 0 + -1.125 = -1.125
-0.75a + a2 = -1.125

The a term is -0.75a.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75a + 0.140625 + a2 = -1.125 + 0.140625

Reorder the terms:
0.140625 + -0.75a + a2 = -1.125 + 0.140625

Combine like terms: -1.125 + 0.140625 = -0.984375
0.140625 + -0.75a + a2 = -0.984375

Factor a perfect square on the left side:
(a + -0.375)(a + -0.375) = -0.984375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}

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