5r+2r-r^2=10

Solution for 5r+2r-r^2=10 equation:

Simplifying
5r + 2r + -1r2 = 10

Combine like terms: 5r + 2r = 7r
7r + -1r2 = 10

Solving
7r + -1r2 = 10

Solving for variable 'r'.

Reorder the terms:
-10 + 7r + -1r2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 7r + -1r2 = 0

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

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

Simplifying
-5 + r = 0

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

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

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

Simplifying
r = 5
Subproblem 2
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
Solution
r = {5, 2}