35=-2r+r^2

Solution for 35=-2r+r^2 equation:

Simplifying
35 = -2r + r2

Solving
35 = -2r + r2

Solving for variable 'r'.

Reorder the terms:
35 + 2r + -1r2 = -2r + 2r + r2 + -1r2

Combine like terms: -2r + 2r = 0
35 + 2r + -1r2 = 0 + r2 + -1r2
35 + 2r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
35 + 2r + -1r2 = 0

Factor a trinomial.
(7 + -1r)(5 + r) = 0

Subproblem 1
Set the factor '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

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

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

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Subproblem 2
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
Solution
r = {7, -5}