5r^2=-9r+2

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

Simplifying
5r2 = -9r + 2

Reorder the terms:
5r2 = 2 + -9r

Solving
5r2 = 2 + -9r

Solving for variable 'r'.

Reorder the terms:
-2 + 9r + 5r2 = 2 + -9r + -2 + 9r

Reorder the terms:
-2 + 9r + 5r2 = 2 + -2 + -9r + 9r

Combine like terms: 2 + -2 = 0
-2 + 9r + 5r2 = 0 + -9r + 9r
-2 + 9r + 5r2 = -9r + 9r

Combine like terms: -9r + 9r = 0
-2 + 9r + 5r2 = 0

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

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

Simplifying
-2 + -1r = 0

Solving
-2 + -1r = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1r = 0 + 2

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

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

Divide each side by '-1'.
r = -2

Simplifying
r = -2
Subproblem 2
Set the factor '(1 + -5r)' equal to zero and attempt to solve:

Simplifying
1 + -5r = 0

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

Combine like terms: 1 + -1 = 0
0 + -5r = 0 + -1
-5r = 0 + -1

Combine like terms: 0 + -1 = -1
-5r = -1

Divide each side by '-5'.
r = 0.2

Simplifying
r = 0.2
Solution
r = {-2, 0.2}