4r^2-9r=-r+5

Solution for 4r^2-9r=-r+5 equation:

Simplifying
4r2 + -9r = -1r + 5

Reorder the terms:
-9r + 4r2 = -1r + 5

Reorder the terms:
-9r + 4r2 = 5 + -1r

Solving
-9r + 4r2 = 5 + -1r

Solving for variable 'r'.

Reorder the terms:
-5 + -9r + r + 4r2 = 5 + -1r + -5 + r

Combine like terms: -9r + r = -8r
-5 + -8r + 4r2 = 5 + -1r + -5 + r

Reorder the terms:
-5 + -8r + 4r2 = 5 + -5 + -1r + r

Combine like terms: 5 + -5 = 0
-5 + -8r + 4r2 = 0 + -1r + r
-5 + -8r + 4r2 = -1r + r

Combine like terms: -1r + r = 0
-5 + -8r + 4r2 = 0

Factor a trinomial.
(-1 + -2r)(5 + -2r) = 0

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

Simplifying
-1 + -2r = 0

Solving
-1 + -2r = 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 + -2r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2r = 0 + 1
-2r = 0 + 1

Combine like terms: 0 + 1 = 1
-2r = 1

Divide each side by '-2'.
r = -0.5

Simplifying
r = -0.5
Subproblem 2
Set the factor '(5 + -2r)' equal to zero and attempt to solve:

Simplifying
5 + -2r = 0

Solving
5 + -2r = 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 + -2r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2r = 0 + -5
-2r = 0 + -5

Combine like terms: 0 + -5 = -5
-2r = -5

Divide each side by '-2'.
r = 2.5

Simplifying
r = 2.5
Solution
r = {-0.5, 2.5}