r^2+6rj-16j^2=

Solution for r^2+6rj-16j^2= equation:

Simplifying
r2 + 6rj + -16j2 = 0

Reorder the terms:
6jr + -16j2 + r2 = 0

Solving
6jr + -16j2 + r2 = 0

Solving for variable 'j'.

Factor a trinomial.
(-8j + -1r)(2j + -1r) = 0

Subproblem 1
Set the factor '(-8j + -1r)' equal to zero and attempt to solve:

Simplifying
-8j + -1r = 0

Solving
-8j + -1r = 0

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

Add 'r' to each side of the equation.
-8j + -1r + r = 0 + r

Combine like terms: -1r + r = 0
-8j + 0 = 0 + r
-8j = 0 + r
Remove the zero:
-8j = r

Divide each side by '-8'.
j = -0.125r

Simplifying
j = -0.125r
Subproblem 2
Set the factor '(2j + -1r)' equal to zero and attempt to solve:

Simplifying
2j + -1r = 0

Solving
2j + -1r = 0

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

Add 'r' to each side of the equation.
2j + -1r + r = 0 + r

Combine like terms: -1r + r = 0
2j + 0 = 0 + r
2j = 0 + r
Remove the zero:
2j = r

Divide each side by '2'.
j = 0.5r

Simplifying
j = 0.5r
Solution
j = {-0.125r, 0.5r}