6r-2r(2-r)=4(2r-1)

Solution for 6r-2r(2-r)=4(2r-1) equation:

Simplifying
6r + -2r(2 + -1r) = 4(2r + -1)
6r + (2 * -2r + -1r * -2r) = 4(2r + -1)
6r + (-4r + 2r2) = 4(2r + -1)

Combine like terms: 6r + -4r = 2r
2r + 2r2 = 4(2r + -1)

Reorder the terms:
2r + 2r2 = 4(-1 + 2r)
2r + 2r2 = (-1 * 4 + 2r * 4)
2r + 2r2 = (-4 + 8r)

Solving
2r + 2r2 = -4 + 8r

Solving for variable 'r'.

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

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

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

Combine like terms: -4 + 4 = 0
4 + -6r + 2r2 = 0 + 8r + -8r
4 + -6r + 2r2 = 8r + -8r

Combine like terms: 8r + -8r = 0
4 + -6r + 2r2 = 0

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

Factor a trinomial.
2((1 + -1r)(2 + -1r)) = 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 '(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 = {1, 2}