3r^2-18r+22=7

Solution for 3r^2-18r+22=7 equation:

Simplifying
3r2 + -18r + 22 = 7

Reorder the terms:
22 + -18r + 3r2 = 7

Solving
22 + -18r + 3r2 = 7

Solving for variable 'r'.

Reorder the terms:
22 + -7 + -18r + 3r2 = 7 + -7

Combine like terms: 22 + -7 = 15
15 + -18r + 3r2 = 7 + -7

Combine like terms: 7 + -7 = 0
15 + -18r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -6r + r2) = 0

Factor a trinomial.
3((1 + -1r)(5 + -1r)) = 0

Ignore the factor 3.
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 '(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 = {1, 5}