6r^2-16r+20=10

Solution for 6r^2-16r+20=10 equation:

Simplifying
6r2 + -16r + 20 = 10

Reorder the terms:
20 + -16r + 6r2 = 10

Solving
20 + -16r + 6r2 = 10

Solving for variable 'r'.

Reorder the terms:
20 + -10 + -16r + 6r2 = 10 + -10

Combine like terms: 20 + -10 = 10
10 + -16r + 6r2 = 10 + -10

Combine like terms: 10 + -10 = 0
10 + -16r + 6r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -8r + 3r2) = 0

Factor a trinomial.
2((1 + -1r)(5 + -3r)) = 0

Ignore the factor 2.
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 + -3r)' equal to zero and attempt to solve:

Simplifying
5 + -3r = 0

Solving
5 + -3r = 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 + -3r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3r = 0 + -5
-3r = 0 + -5

Combine like terms: 0 + -5 = -5
-3r = -5

Divide each side by '-3'.
r = 1.666666667

Simplifying
r = 1.666666667
Solution
r = {1, 1.666666667}