r^2+8rf+7f^2=

Solution for r^2+8rf+7f^2= equation:

Simplifying
r2 + 8rf + 7f2 = 0

Reorder the terms:
8fr + 7f2 + r2 = 0

Solving
8fr + 7f2 + r2 = 0

Solving for variable 'f'.

Factor a trinomial.
(7f + r)(f + r) = 0

Subproblem 1
Set the factor '(7f + r)' equal to zero and attempt to solve:

Simplifying
7f + r = 0

Solving
7f + r = 0

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

Add '-1r' to each side of the equation.
7f + r + -1r = 0 + -1r

Combine like terms: r + -1r = 0
7f + 0 = 0 + -1r
7f = 0 + -1r
Remove the zero:
7f = -1r

Divide each side by '7'.
f = -0.1428571429r

Simplifying
f = -0.1428571429r
Subproblem 2
Set the factor '(f + r)' equal to zero and attempt to solve:

Simplifying
f + r = 0

Solving
f + r = 0

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

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

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

Simplifying
f = -1r
Solution
f = {-0.1428571429r, -1r}