r^2=5r-4

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

Simplifying
r2 = 5r + -4

Reorder the terms:
r2 = -4 + 5r

Solving
r2 = -4 + 5r

Solving for variable 'r'.

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

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

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

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

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

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

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

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

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

Simplifying
r = 4
Solution
r = {1, 4}