r^2-4r+10=6

Solution for r^2-4r+10=6 equation:

Simplifying
r2 + -4r + 10 = 6

Reorder the terms:
10 + -4r + r2 = 6

Solving
10 + -4r + r2 = 6

Solving for variable 'r'.

Reorder the terms:
10 + -6 + -4r + r2 = 6 + -6

Combine like terms: 10 + -6 = 4
4 + -4r + r2 = 6 + -6

Combine like terms: 6 + -6 = 0
4 + -4r + r2 = 0

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

Subproblem 1
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
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 = {2, 2}