33q^3+33q^2r+33qr^2=

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Solution for 33q^3+33q^2r+33qr^2= equation: 


Simplifying
33q3 + 33q2r + 33qr2 = 0

Reorder the terms:
33qr2 + 33q2r + 33q3 = 0

Solving
33qr2 + 33q2r + 33q3 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '33q'.
33q(r2 + qr + q2) = 0

Ignore the factor 33.

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 '(r2 + qr + q2)' equal to zero and attempt to solve:

Simplifying
r2 + qr + q2 = 0

Reorder the terms:
qr + q2 + r2 = 0

Solving
qr + q2 + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1r2' to each side of the equation.
qr + q2 + r2 + -1r2 = 0 + -1r2

Combine like terms: r2 + -1r2 = 0
qr + q2 + 0 = 0 + -1r2
qr + q2 = 0 + -1r2
Remove the zero:
qr + q2 = -1r2

The q term is qr.  Take half its coefficient (0.5r).
Square it (0.25r2) and add it to both sides.

Add '0.25r2' to each side of the equation.
qr + q2 + 0.25r2 = -1r2 + 0.25r2

Combine like terms: -1r2 + 0.25r2 = -0.75r2
qr + q2 + 0.25r2 = -0.75r2

Factor a perfect square on the left side:
(q + 0.5r)(q + 0.5r) = -0.75r2

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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