b^2+6b-3=0

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

Simplifying
b2 + 6b + -3 = 0

Reorder the terms:
-3 + 6b + b2 = 0

Solving
-3 + 6b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 6b + 3 + b2 = 0 + 3

Reorder the terms:
-3 + 3 + 6b + b2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 6b + b2 = 0 + 3
6b + b2 = 0 + 3

Combine like terms: 0 + 3 = 3
6b + b2 = 3

The b term is 6b.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6b + 9 + b2 = 3 + 9

Reorder the terms:
9 + 6b + b2 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + 6b + b2 = 12

Factor a perfect square on the left side:
(b + 3)(b + 3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(b + 3) equal to 3.464101615 and -3.464101615.

Subproblem 1
b + 3 = 3.464101615

Simplifying
b + 3 = 3.464101615

Reorder the terms:
3 + b = 3.464101615

Solving
3 + b = 3.464101615

Solving for variable 'b'.

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

Add '-3' to each side of the equation.
3 + -3 + b = 3.464101615 + -3

Combine like terms: 3 + -3 = 0
0 + b = 3.464101615 + -3
b = 3.464101615 + -3

Combine like terms: 3.464101615 + -3 = 0.464101615
b = 0.464101615

Simplifying
b = 0.464101615

Subproblem 2
b + 3 = -3.464101615

Simplifying
b + 3 = -3.464101615

Reorder the terms:
3 + b = -3.464101615

Solving
3 + b = -3.464101615

Solving for variable 'b'.

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

Add '-3' to each side of the equation.
3 + -3 + b = -3.464101615 + -3

Combine like terms: 3 + -3 = 0
0 + b = -3.464101615 + -3
b = -3.464101615 + -3

Combine like terms: -3.464101615 + -3 = -6.464101615
b = -6.464101615

Simplifying
b = -6.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.464101615, -6.464101615}