Q^3-21Q^2+500Q=0

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Solution for Q^3-21Q^2+500Q=0 equation: 


Simplifying
Q3 + -21Q2 + 500Q = 0

Reorder the terms:
500Q + -21Q2 + Q3 = 0

Solving
500Q + -21Q2 + Q3 = 0

Solving for variable 'Q'.

Factor out the Greatest Common Factor (GCF), 'Q'.
Q(500 + -21Q + Q2) = 0


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

Simplifying
Q = 0

Solving
Q = 0

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

Simplifying
Q = 0

Subproblem 2
Set the factor '(500 + -21Q + Q2)' equal to zero and attempt to solve:

Simplifying
500 + -21Q + Q2 = 0

Solving
500 + -21Q + Q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-500' to each side of the equation.
500 + -21Q + -500 + Q2 = 0 + -500

Reorder the terms:
500 + -500 + -21Q + Q2 = 0 + -500

Combine like terms: 500 + -500 = 0
0 + -21Q + Q2 = 0 + -500
-21Q + Q2 = 0 + -500

Combine like terms: 0 + -500 = -500
-21Q + Q2 = -500

The Q term is -21Q.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21Q + 110.25 + Q2 = -500 + 110.25

Reorder the terms:
110.25 + -21Q + Q2 = -500 + 110.25

Combine like terms: -500 + 110.25 = -389.75
110.25 + -21Q + Q2 = -389.75

Factor a perfect square on the left side:
(Q + -10.5)(Q + -10.5) = -389.75

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
Q = {0}

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