12x^4-15x^3+18x^2=0

Solution for 12x^4-15x^3+18x^2=0 equation:

Simplifying
12x4 + -15x3 + 18x2 = 0

Reorder the terms:
18x2 + -15x3 + 12x4 = 0

Solving
18x2 + -15x3 + 12x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(6 + -5x + 4x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(6 + -5x + 4x2)' equal to zero and attempt to solve:

Simplifying
6 + -5x + 4x2 = 0

Solving
6 + -5x + 4x2 = 0

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

Divide each side by '4'.
1.5 + -1.25x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -1.25x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -1.25x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -1.25x + x2 = 0 + -1.5
-1.25x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-1.25x + x2 = -1.5

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = -1.5 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = -1.5 + 0.390625

Combine like terms: -1.5 + 0.390625 = -1.109375
0.390625 + -1.25x + x2 = -1.109375

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = -1.109375

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}