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

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

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

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

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

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

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

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

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

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

Solving
6 + 2r + 3r2 = 0

Solving for variable 'r'.

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

Divide each side by '3'.
2 + 0.6666666667r + r2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 0.6666666667r + -2 + r2 = 0 + -2

Reorder the terms:
2 + -2 + 0.6666666667r + r2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 0.6666666667r + r2 = 0 + -2
0.6666666667r + r2 = 0 + -2

Combine like terms: 0 + -2 = -2
0.6666666667r + r2 = -2

The r term is 0.6666666667r.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667r + 0.1111111112 + r2 = -2 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667r + r2 = -2 + 0.1111111112

Combine like terms: -2 + 0.1111111112 = -1.8888888888
0.1111111112 + 0.6666666667r + r2 = -1.8888888888

Factor a perfect square on the left side:
(r + 0.3333333334)(r + 0.3333333334) = -1.8888888888

Can't calculate square root of the right side.

The solution to this equation could not be determined.