-r^2+5r-4=0

Solution for -r^2+5r-4=0 equation:

Simplifying
-1r2 + 5r + -4 = 0

Reorder the terms:
-4 + 5r + -1r2 = 0

Solving
-4 + 5r + -1r2 = 0

Solving for variable 'r'.

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

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

Simplifying
-4 + r = 0

Solving
-4 + r = 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 + r = 0 + 4

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

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

Simplifying
r = 4
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 = {4, 1}