r^2=5-4r

Solution for r^2=5-4r equation:

Simplifying
r2 = 5 + -4r

Solving
r2 = 5 + -4r

Solving for variable 'r'.

Reorder the terms:
-5 + 4r + r2 = 5 + -4r + -5 + 4r

Reorder the terms:
-5 + 4r + r2 = 5 + -5 + -4r + 4r

Combine like terms: 5 + -5 = 0
-5 + 4r + r2 = 0 + -4r + 4r
-5 + 4r + r2 = -4r + 4r

Combine like terms: -4r + 4r = 0
-5 + 4r + r2 = 0

Factor a trinomial.
(-5 + -1r)(1 + -1r) = 0

Subproblem 1
Set the factor '(-5 + -1r)' equal to zero and attempt to solve:

Simplifying
-5 + -1r = 0

Solving
-5 + -1r = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1r = 0 + 5
-1r = 0 + 5

Combine like terms: 0 + 5 = 5
-1r = 5

Divide each side by '-1'.
r = -5

Simplifying
r = -5
Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1r = 0 + -1
-1r = 0 + -1

Combine like terms: 0 + -1 = -1
-1r = -1

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

Simplifying
r = 1
Solution
r = {-5, 1}