r^2=-4r+12

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

Simplifying
r2 = -4r + 12

Reorder the terms:
r2 = 12 + -4r

Solving
r2 = 12 + -4r

Solving for variable 'r'.

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

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

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

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

Factor a trinomial.
(-6 + -1r)(2 + -1r) = 0

Subproblem 1
Set the factor '(-6 + -1r)' equal to zero and attempt to solve:

Simplifying
-6 + -1r = 0

Solving
-6 + -1r = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1r = 0 + 6

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

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

Divide each side by '-1'.
r = -6

Simplifying
r = -6
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 = {-6, 2}