12x^3-18x^2+40x=

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Solution for 12x^3-18x^2+40x= equation: 


Simplifying
12x3 + -18x2 + 40x = 0

Reorder the terms:
40x + -18x2 + 12x3 = 0

Solving
40x + -18x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(20 + -9x + 6x2) = 0

Ignore the factor 2.

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(20 + -9x + 6x2)' equal to zero and attempt to solve:

Simplifying
20 + -9x + 6x2 = 0

Solving
20 + -9x + 6x2 = 0

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

Divide each side by '6'.
3.333333333 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -1.5x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -1.5x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -1.5x + x2 = 0 + -3.333333333
-1.5x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-1.5x + x2 = -3.333333333

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -3.333333333 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -3.333333333 + 0.5625

Combine like terms: -3.333333333 + 0.5625 = -2.770833333
0.5625 + -1.5x + x2 = -2.770833333

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = -2.770833333

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
x = {0}

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