2r^2-5r+4=r^2

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

Simplifying
2r2 + -5r + 4 = r2

Reorder the terms:
4 + -5r + 2r2 = r2

Solving
4 + -5r + 2r2 = r2

Solving for variable 'r'.

Combine like terms: 2r2 + -1r2 = 1r2
4 + -5r + 1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
4 + -5r + 1r2 = 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}