r^2-8r+10=3

Solution for r^2-8r+10=3 equation:

Simplifying
r2 + -8r + 10 = 3

Reorder the terms:
10 + -8r + r2 = 3

Solving
10 + -8r + r2 = 3

Solving for variable 'r'.

Reorder the terms:
10 + -3 + -8r + r2 = 3 + -3

Combine like terms: 10 + -3 = 7
7 + -8r + r2 = 3 + -3

Combine like terms: 3 + -3 = 0
7 + -8r + r2 = 0

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

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

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

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

Simplifying
r = 1
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 = {1, 7}