4r^2=12-2r

Solution for 4r^2=12-2r equation:

Simplifying
4r2 = 12 + -2r

Solving
4r2 = 12 + -2r

Solving for variable 'r'.

Reorder the terms:
-12 + 2r + 4r2 = 12 + -2r + -12 + 2r

Reorder the terms:
-12 + 2r + 4r2 = 12 + -12 + -2r + 2r

Combine like terms: 12 + -12 = 0
-12 + 2r + 4r2 = 0 + -2r + 2r
-12 + 2r + 4r2 = -2r + 2r

Combine like terms: -2r + 2r = 0
-12 + 2r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + r + 2r2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
r = {-2, 1.5}