2r^2-5r=-1-2r^2

Solution for 2r^2-5r=-1-2r^2 equation:

Simplifying
2r2 + -5r = -1 + -2r2

Reorder the terms:
-5r + 2r2 = -1 + -2r2

Solving
-5r + 2r2 = -1 + -2r2

Solving for variable 'r'.

Reorder the terms:
1 + -5r + 2r2 + 2r2 = -1 + -2r2 + 1 + 2r2

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

Reorder the terms:
1 + -5r + 4r2 = -1 + 1 + -2r2 + 2r2

Combine like terms: -1 + 1 = 0
1 + -5r + 4r2 = 0 + -2r2 + 2r2
1 + -5r + 4r2 = -2r2 + 2r2

Combine like terms: -2r2 + 2r2 = 0
1 + -5r + 4r2 = 0

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

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

Simplifying
1 + -4r = 0

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

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

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

Divide each side by '-4'.
r = 0.25

Simplifying
r = 0.25
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 = {0.25, 1}