6b^2+6b-21=-4

Solution for 6b^2+6b-21=-4 equation:

Simplifying
6b2 + 6b + -21 = -4

Reorder the terms:
-21 + 6b + 6b2 = -4

Solving
-21 + 6b + 6b2 = -4

Solving for variable 'b'.

Reorder the terms:
-21 + 4 + 6b + 6b2 = -4 + 4

Combine like terms: -21 + 4 = -17
-17 + 6b + 6b2 = -4 + 4

Combine like terms: -4 + 4 = 0
-17 + 6b + 6b2 = 0

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

Divide each side by '6'.
-2.833333333 + b + b2 = 0

Move the constant term to the right:

Add '2.833333333' to each side of the equation.
-2.833333333 + b + 2.833333333 + b2 = 0 + 2.833333333

Reorder the terms:
-2.833333333 + 2.833333333 + b + b2 = 0 + 2.833333333

Combine like terms: -2.833333333 + 2.833333333 = 0.000000000
0.000000000 + b + b2 = 0 + 2.833333333
b + b2 = 0 + 2.833333333

Combine like terms: 0 + 2.833333333 = 2.833333333
b + b2 = 2.833333333

The b term is b.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + b2 = 2.833333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + b2 = 2.833333333 + 0.25

Combine like terms: 2.833333333 + 0.25 = 3.083333333
1.25 + b2 = 3.083333333

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 3.083333333

Calculate the square root of the right side: 1.755942292

Break this problem into two subproblems by setting 
(b + 0.5) equal to 1.755942292 and -1.755942292.

Subproblem 1
b + 0.5 = 1.755942292

Simplifying
b + 0.5 = 1.755942292

Reorder the terms:
0.5 + b = 1.755942292

Solving
0.5 + b = 1.755942292

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b = 1.755942292 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = 1.755942292 + -0.5
b = 1.755942292 + -0.5

Combine like terms: 1.755942292 + -0.5 = 1.255942292
b = 1.255942292

Simplifying
b = 1.255942292

Subproblem 2
b + 0.5 = -1.755942292

Simplifying
b + 0.5 = -1.755942292

Reorder the terms:
0.5 + b = -1.755942292

Solving
0.5 + b = -1.755942292

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b = -1.755942292 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = -1.755942292 + -0.5
b = -1.755942292 + -0.5

Combine like terms: -1.755942292 + -0.5 = -2.255942292
b = -2.255942292

Simplifying
b = -2.255942292

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.255942292, -2.255942292}