24+22r=10r^2

Solution for 24+22r=10r^2 equation:

Simplifying
24 + 22r = 10r2

Solving
24 + 22r = 10r2

Solving for variable 'r'.

Combine like terms: 10r2 + -10r2 = 0
24 + 22r + -10r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 11r + -5r2) = 0

Factor a trinomial.
2((3 + -1r)(4 + 5r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Subproblem 2
Set the factor '(4 + 5r)' equal to zero and attempt to solve:

Simplifying
4 + 5r = 0

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

Combine like terms: 4 + -4 = 0
0 + 5r = 0 + -4
5r = 0 + -4

Combine like terms: 0 + -4 = -4
5r = -4

Divide each side by '5'.
r = -0.8

Simplifying
r = -0.8
Solution
r = {3, -0.8}