-r^2+10r-21=0

Solution for -r^2+10r-21=0 equation:

Simplifying
-1r2 + 10r + -21 = 0

Reorder the terms:
-21 + 10r + -1r2 = 0

Solving
-21 + 10r + -1r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-7 + r)(3 + -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 '(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
Solution
r = {7, 3}