24x(x)(x)(x)-15x(x)(x)+3x(x)=0

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Solution for 24x(x)(x)(x)-15x(x)(x)+3x(x)=0 equation: 


Simplifying
24x(x)(x)(x) + -15x(x)(x) + 3x(x) = 0

Multiply x * x
24x2 * x * x + -15x(x)(x) + 3x(x) = 0

Multiply x2 * x
24x3 * x + -15x(x)(x) + 3x(x) = 0

Multiply x3 * x
24x4 + -15x(x)(x) + 3x(x) = 0

Multiply x * x
24x4 + -15x2 * x + 3x(x) = 0

Multiply x2 * x
24x4 + -15x3 + 3x(x) = 0

Multiply x * x
24x4 + -15x3 + 3x2 = 0

Reorder the terms:
3x2 + -15x3 + 24x4 = 0

Solving
3x2 + -15x3 + 24x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(1 + -5x + 8x2) = 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 '(1 + -5x + 8x2)' equal to zero and attempt to solve:

Simplifying
1 + -5x + 8x2 = 0

Solving
1 + -5x + 8x2 = 0

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

Divide each side by '8'.
0.125 + -0.625x + x2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -0.625x + -0.125 + x2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -0.625x + x2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -0.625x + x2 = 0 + -0.125
-0.625x + x2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-0.625x + x2 = -0.125

The x term is -0.625x.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625x + 0.09765625 + x2 = -0.125 + 0.09765625

Reorder the terms:
0.09765625 + -0.625x + x2 = -0.125 + 0.09765625

Combine like terms: -0.125 + 0.09765625 = -0.02734375
0.09765625 + -0.625x + x2 = -0.02734375

Factor a perfect square on the left side:
(x + -0.3125)(x + -0.3125) = -0.02734375

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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