3x^2+2rx-r^2=0

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Solution for 3x^2+2rx-r^2=0 equation: 


Simplifying
3x2 + 2rx + -1r2 = 0

Reorder the terms:
2rx + -1r2 + 3x2 = 0

Solving
2rx + -1r2 + 3x2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1r + -1x)(r + -3x) = 0


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

Simplifying
-1r + -1x = 0

Solving
-1r + -1x = 0

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

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

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

Divide each side by '-1'.
r = -1x

Simplifying
r = -1x

Subproblem 2
Set the factor '(r + -3x)' equal to zero and attempt to solve:

Simplifying
r + -3x = 0

Solving
r + -3x = 0

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

Add '3x' to each side of the equation.
r + -3x + 3x = 0 + 3x

Combine like terms: -3x + 3x = 0
r + 0 = 0 + 3x
r = 0 + 3x
Remove the zero:
r = 3x

Simplifying
r = 3x
Solution
r = {-1x, 3x}

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