-r^2+12r=35

Solution for -r^2+12r=35 equation:

Simplifying
-1r2 + 12r = 35

Reorder the terms:
12r + -1r2 = 35

Solving
12r + -1r2 = 35

Solving for variable 'r'.

Reorder the terms:
-35 + 12r + -1r2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + 12r + -1r2 = 0

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

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

Simplifying
-7 + r = 0

Solving
-7 + r = 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 + r = 0 + 7

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

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

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