.5(4r^2-2r)=6

Solution for .5(4r^2-2r)=6 equation:

Simplifying
0.5(4r2 + -2r) = 6

Reorder the terms:
0.5(-2r + 4r2) = 6
(-2r * 0.5 + 4r2 * 0.5) = 6
(-1r + 2r2) = 6

Solving
-1r + 2r2 = 6

Solving for variable 'r'.

Reorder the terms:
-6 + -1r + 2r2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -1r + 2r2 = 0

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

Subproblem 1
Set the factor '(-3 + -2r)' equal to zero and attempt to solve:

Simplifying
-3 + -2r = 0

Solving
-3 + -2r = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2r = 0 + 3
-2r = 0 + 3

Combine like terms: 0 + 3 = 3
-2r = 3

Divide each side by '-2'.
r = -1.5

Simplifying
r = -1.5
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 = {-1.5, 2}