r^2+3r-6=0

Solution for r^2+3r-6=0 equation:

Simplifying
r2 + 3r + -6 = 0

Reorder the terms:
-6 + 3r + r2 = 0

Solving
-6 + 3r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3r + 6 + r2 = 0 + 6

Reorder the terms:
-6 + 6 + 3r + r2 = 0 + 6

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

Combine like terms: 0 + 6 = 6
3r + r2 = 6

The r term is 3r.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3r + 2.25 + r2 = 6 + 2.25

Reorder the terms:
2.25 + 3r + r2 = 6 + 2.25

Combine like terms: 6 + 2.25 = 8.25
2.25 + 3r + r2 = 8.25

Factor a perfect square on the left side:
(r + 1.5)(r + 1.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(r + 1.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
r + 1.5 = 2.872281323

Simplifying
r + 1.5 = 2.872281323

Reorder the terms:
1.5 + r = 2.872281323

Solving
1.5 + r = 2.872281323

Solving for variable 'r'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = 2.872281323 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = 2.872281323 + -1.5
r = 2.872281323 + -1.5

Combine like terms: 2.872281323 + -1.5 = 1.372281323
r = 1.372281323

Simplifying
r = 1.372281323

Subproblem 2
r + 1.5 = -2.872281323

Simplifying
r + 1.5 = -2.872281323

Reorder the terms:
1.5 + r = -2.872281323

Solving
1.5 + r = -2.872281323

Solving for variable 'r'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = -2.872281323 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = -2.872281323 + -1.5
r = -2.872281323 + -1.5

Combine like terms: -2.872281323 + -1.5 = -4.372281323
r = -4.372281323

Simplifying
r = -4.372281323

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.372281323, -4.372281323}