q^2+11qr+18r^2=0

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Solution for q^2+11qr+18r^2=0 equation: 


Simplifying
q2 + 11qr + 18r2 = 0

Reorder the terms:
11qr + q2 + 18r2 = 0

Solving
11qr + q2 + 18r2 = 0

Solving for variable 'q'.

Factor a trinomial.
(q + 2r)(q + 9r) = 0


Subproblem 1
Set the factor '(q + 2r)' equal to zero and attempt to solve:

Simplifying
q + 2r = 0

Solving
q + 2r = 0

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

Add '-2r' to each side of the equation.
q + 2r + -2r = 0 + -2r

Combine like terms: 2r + -2r = 0
q + 0 = 0 + -2r
q = 0 + -2r
Remove the zero:
q = -2r

Simplifying
q = -2r

Subproblem 2
Set the factor '(q + 9r)' equal to zero and attempt to solve:

Simplifying
q + 9r = 0

Solving
q + 9r = 0

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

Add '-9r' to each side of the equation.
q + 9r + -9r = 0 + -9r

Combine like terms: 9r + -9r = 0
q + 0 = 0 + -9r
q = 0 + -9r
Remove the zero:
q = -9r

Simplifying
q = -9r
Solution
q = {-2r, -9r}

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