(4r^2-6r+2)-(-r^2+3r+5)=

Solution for (4r^2-6r+2)-(-r^2+3r+5)= equation:

Simplifying
(4r2 + -6r + 2) + -1(-1r2 + 3r + 5) = 0

Reorder the terms:
(2 + -6r + 4r2) + -1(-1r2 + 3r + 5) = 0

Remove parenthesis around (2 + -6r + 4r2)
2 + -6r + 4r2 + -1(-1r2 + 3r + 5) = 0

Reorder the terms:
2 + -6r + 4r2 + -1(5 + 3r + -1r2) = 0
2 + -6r + 4r2 + (5 * -1 + 3r * -1 + -1r2 * -1) = 0
2 + -6r + 4r2 + (-5 + -3r + 1r2) = 0

Reorder the terms:
2 + -5 + -6r + -3r + 4r2 + 1r2 = 0

Combine like terms: 2 + -5 = -3
-3 + -6r + -3r + 4r2 + 1r2 = 0

Combine like terms: -6r + -3r = -9r
-3 + -9r + 4r2 + 1r2 = 0

Combine like terms: 4r2 + 1r2 = 5r2
-3 + -9r + 5r2 = 0

Solving
-3 + -9r + 5r2 = 0

Solving for variable 'r'.

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

Divide each side by '5'.
-0.6 + -1.8r + r2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -1.8r + 0.6 + r2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -1.8r + r2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -1.8r + r2 = 0 + 0.6
-1.8r + r2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-1.8r + r2 = 0.6

The r term is -1.8r.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8r + 0.81 + r2 = 0.6 + 0.81

Reorder the terms:
0.81 + -1.8r + r2 = 0.6 + 0.81

Combine like terms: 0.6 + 0.81 = 1.41
0.81 + -1.8r + r2 = 1.41

Factor a perfect square on the left side:
(r + -0.9)(r + -0.9) = 1.41

Calculate the square root of the right side: 1.187434209

Break this problem into two subproblems by setting 
(r + -0.9) equal to 1.187434209 and -1.187434209.

Subproblem 1
r + -0.9 = 1.187434209

Simplifying
r + -0.9 = 1.187434209

Reorder the terms:
-0.9 + r = 1.187434209

Solving
-0.9 + r = 1.187434209

Solving for variable 'r'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + r = 1.187434209 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + r = 1.187434209 + 0.9
r = 1.187434209 + 0.9

Combine like terms: 1.187434209 + 0.9 = 2.087434209
r = 2.087434209

Simplifying
r = 2.087434209

Subproblem 2
r + -0.9 = -1.187434209

Simplifying
r + -0.9 = -1.187434209

Reorder the terms:
-0.9 + r = -1.187434209

Solving
-0.9 + r = -1.187434209

Solving for variable 'r'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + r = -1.187434209 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + r = -1.187434209 + 0.9
r = -1.187434209 + 0.9

Combine like terms: -1.187434209 + 0.9 = -0.287434209
r = -0.287434209

Simplifying
r = -0.287434209

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.087434209, -0.287434209}