8r-4r+2=6r^2

Solution for 8r-4r+2=6r^2 equation:

Simplifying
8r + -4r + 2 = 6r2

Reorder the terms:
2 + 8r + -4r = 6r2

Combine like terms: 8r + -4r = 4r
2 + 4r = 6r2

Solving
2 + 4r = 6r2

Solving for variable 'r'.

Combine like terms: 6r2 + -6r2 = 0
2 + 4r + -6r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 2r + -3r2) = 0

Factor a trinomial.
2((1 + -1r)(1 + 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 '(1 + 3r)' equal to zero and attempt to solve:

Simplifying
1 + 3r = 0

Solving
1 + 3r = 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 + 3r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3r = 0 + -1
3r = 0 + -1

Combine like terms: 0 + -1 = -1
3r = -1

Divide each side by '3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
Solution
r = {1, -0.3333333333}