24x^2+2xr-r^2=0

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Solution for 24x^2+2xr-r^2=0 equation: 


Simplifying
24x2 + 2xr + -1r2 = 0

Reorder the terms:
2rx + -1r2 + 24x2 = 0

Solving
2rx + -1r2 + 24x2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1r + -4x)(r + -6x) = 0


Subproblem 1
Set the factor '(-1r + -4x)' equal to zero and attempt to solve:

Simplifying
-1r + -4x = 0

Solving
-1r + -4x = 0

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

Add '4x' to each side of the equation.
-1r + -4x + 4x = 0 + 4x

Combine like terms: -4x + 4x = 0
-1r + 0 = 0 + 4x
-1r = 0 + 4x
Remove the zero:
-1r = 4x

Divide each side by '-1'.
r = -4x

Simplifying
r = -4x

Subproblem 2
Set the factor '(r + -6x)' equal to zero and attempt to solve:

Simplifying
r + -6x = 0

Solving
r + -6x = 0

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

Add '6x' to each side of the equation.
r + -6x + 6x = 0 + 6x

Combine like terms: -6x + 6x = 0
r + 0 = 0 + 6x
r = 0 + 6x
Remove the zero:
r = 6x

Simplifying
r = 6x
Solution
r = {-4x, 6x}

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