2(b^2+3b-14)=0

Solution for 2(b^2+3b-14)=0 equation:

Simplifying
2(b2 + 3b + -14) = 0

Reorder the terms:
2(-14 + 3b + b2) = 0
(-14 * 2 + 3b * 2 + b2 * 2) = 0
(-28 + 6b + 2b2) = 0

Solving
-28 + 6b + 2b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 3b + b2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-14 + 3b + b2)' equal to zero and attempt to solve:

Simplifying
-14 + 3b + b2 = 0

Solving
-14 + 3b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 3b + 14 + b2 = 0 + 14

Reorder the terms:
-14 + 14 + 3b + b2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 3b + b2 = 0 + 14
3b + b2 = 0 + 14

Combine like terms: 0 + 14 = 14
3b + b2 = 14

The b term is 3b.  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.
3b + 2.25 + b2 = 14 + 2.25

Reorder the terms:
2.25 + 3b + b2 = 14 + 2.25

Combine like terms: 14 + 2.25 = 16.25
2.25 + 3b + b2 = 16.25

Factor a perfect square on the left side:
(b + 1.5)(b + 1.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(b + 1.5) equal to 4.031128874 and -4.031128874.

Subproblem 1
b + 1.5 = 4.031128874

Simplifying
b + 1.5 = 4.031128874

Reorder the terms:
1.5 + b = 4.031128874

Solving
1.5 + b = 4.031128874

Solving for variable 'b'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + b = 4.031128874 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + b = 4.031128874 + -1.5
b = 4.031128874 + -1.5

Combine like terms: 4.031128874 + -1.5 = 2.531128874
b = 2.531128874

Simplifying
b = 2.531128874

Subproblem 2
b + 1.5 = -4.031128874

Simplifying
b + 1.5 = -4.031128874

Reorder the terms:
1.5 + b = -4.031128874

Solving
1.5 + b = -4.031128874

Solving for variable 'b'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + b = -4.031128874 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + b = -4.031128874 + -1.5
b = -4.031128874 + -1.5

Combine like terms: -4.031128874 + -1.5 = -5.531128874
b = -5.531128874

Simplifying
b = -5.531128874

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {2.531128874, -5.531128874}
Solution
b = {2.531128874, -5.531128874}