q^2+3qr-4r^2=0

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Solution for q^2+3qr-4r^2=0 equation: 


Simplifying
q2 + 3qr + -4r2 = 0

Reorder the terms:
3qr + q2 + -4r2 = 0

Solving
3qr + q2 + -4r2 = 0

Solving for variable 'q'.

Factor a trinomial.
(q + -1r)(q + 4r) = 0


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

Simplifying
q + -1r = 0

Solving
q + -1r = 0

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

Add 'r' to each side of the equation.
q + -1r + r = 0 + r

Combine like terms: -1r + r = 0
q + 0 = 0 + r
q = 0 + r
Remove the zero:
q = r

Simplifying
q = r

Subproblem 2
Set the factor '(q + 4r)' equal to zero and attempt to solve:

Simplifying
q + 4r = 0

Solving
q + 4r = 0

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

Add '-4r' to each side of the equation.
q + 4r + -4r = 0 + -4r

Combine like terms: 4r + -4r = 0
q + 0 = 0 + -4r
q = 0 + -4r
Remove the zero:
q = -4r

Simplifying
q = -4r
Solution
q = {r, -4r}

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