5r(r-1)=2(r-4)-6

Solution for 5r(r-1)=2(r-4)-6 equation:

Simplifying
5r(r + -1) = 2(r + -4) + -6

Reorder the terms:
5r(-1 + r) = 2(r + -4) + -6
(-1 * 5r + r * 5r) = 2(r + -4) + -6
(-5r + 5r2) = 2(r + -4) + -6

Reorder the terms:
-5r + 5r2 = 2(-4 + r) + -6
-5r + 5r2 = (-4 * 2 + r * 2) + -6
-5r + 5r2 = (-8 + 2r) + -6

Reorder the terms:
-5r + 5r2 = -8 + -6 + 2r

Combine like terms: -8 + -6 = -14
-5r + 5r2 = -14 + 2r

Solving
-5r + 5r2 = -14 + 2r

Solving for variable 'r'.

Reorder the terms:
14 + -5r + -2r + 5r2 = -14 + 2r + 14 + -2r

Combine like terms: -5r + -2r = -7r
14 + -7r + 5r2 = -14 + 2r + 14 + -2r

Reorder the terms:
14 + -7r + 5r2 = -14 + 14 + 2r + -2r

Combine like terms: -14 + 14 = 0
14 + -7r + 5r2 = 0 + 2r + -2r
14 + -7r + 5r2 = 2r + -2r

Combine like terms: 2r + -2r = 0
14 + -7r + 5r2 = 0

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

Divide each side by '5'.
2.8 + -1.4r + r2 = 0

Move the constant term to the right:

Add '-2.8' to each side of the equation.
2.8 + -1.4r + -2.8 + r2 = 0 + -2.8

Reorder the terms:
2.8 + -2.8 + -1.4r + r2 = 0 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + -1.4r + r2 = 0 + -2.8
-1.4r + r2 = 0 + -2.8

Combine like terms: 0 + -2.8 = -2.8
-1.4r + r2 = -2.8

The r term is -1.4r.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4r + 0.49 + r2 = -2.8 + 0.49

Reorder the terms:
0.49 + -1.4r + r2 = -2.8 + 0.49

Combine like terms: -2.8 + 0.49 = -2.31
0.49 + -1.4r + r2 = -2.31

Factor a perfect square on the left side:
(r + -0.7)(r + -0.7) = -2.31

Can't calculate square root of the right side.

The solution to this equation could not be determined.