20x^4-10x^3+15x^2=

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Solution for 20x^4-10x^3+15x^2= equation: 


Simplifying
20x4 + -10x3 + 15x2 = 0

Reorder the terms:
15x2 + -10x3 + 20x4 = 0

Solving
15x2 + -10x3 + 20x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x2'.
5x2(3 + -2x + 4x2) = 0

Ignore the factor 5.

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 '(3 + -2x + 4x2)' equal to zero and attempt to solve:

Simplifying
3 + -2x + 4x2 = 0

Solving
3 + -2x + 4x2 = 0

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

Divide each side by '4'.
0.75 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -0.5x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -0.5x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -0.5x + x2 = 0 + -0.75
-0.5x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-0.5x + x2 = -0.75

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -0.75 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -0.75 + 0.0625

Combine like terms: -0.75 + 0.0625 = -0.6875
0.0625 + -0.5x + x2 = -0.6875

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -0.6875

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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