r(r-2)=35

Solution for r(r-2)=35 equation:

Simplifying
r(r + -2) = 35

Reorder the terms:
r(-2 + r) = 35
(-2 * r + r * r) = 35
(-2r + r2) = 35

Solving
-2r + r2 = 35

Solving for variable 'r'.

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

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

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

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

Simplifying
-5 + -1r = 0

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

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

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

Divide each side by '-1'.
r = -5

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