4r-6=r^2

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

Simplifying
4r + -6 = r2

Reorder the terms:
-6 + 4r = r2

Solving
-6 + 4r = r2

Solving for variable 'r'.

Combine like terms: r2 + -1r2 = 0
-6 + 4r + -1r2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
6 + -4r + r2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -4r + -6 + r2 = 0 + -6

Reorder the terms:
6 + -6 + -4r + r2 = 0 + -6

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

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

The r term is -4r.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4r + 4 + r2 = -6 + 4

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

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

Factor a perfect square on the left side:
(r + -2)(r + -2) = -2

Can't calculate square root of the right side.

The solution to this equation could not be determined.