2b(b^2+4b+8)-3b(3b^2+9b-18)=0

Solution for 2b(b^2+4b+8)-3b(3b^2+9b-18)=0 equation:

Simplifying
2b(b2 + 4b + 8) + -3b(3b2 + 9b + -18) = 0

Reorder the terms:
2b(8 + 4b + b2) + -3b(3b2 + 9b + -18) = 0
(8 * 2b + 4b * 2b + b2 * 2b) + -3b(3b2 + 9b + -18) = 0
(16b + 8b2 + 2b3) + -3b(3b2 + 9b + -18) = 0

Reorder the terms:
16b + 8b2 + 2b3 + -3b(-18 + 9b + 3b2) = 0
16b + 8b2 + 2b3 + (-18 * -3b + 9b * -3b + 3b2 * -3b) = 0
16b + 8b2 + 2b3 + (54b + -27b2 + -9b3) = 0

Reorder the terms:
16b + 54b + 8b2 + -27b2 + 2b3 + -9b3 = 0

Combine like terms: 16b + 54b = 70b
70b + 8b2 + -27b2 + 2b3 + -9b3 = 0

Combine like terms: 8b2 + -27b2 = -19b2
70b + -19b2 + 2b3 + -9b3 = 0

Combine like terms: 2b3 + -9b3 = -7b3
70b + -19b2 + -7b3 = 0

Solving
70b + -19b2 + -7b3 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), 'b'.
b(70 + -19b + -7b2) = 0

Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

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

Simplifying
b = 0
Subproblem 2
Set the factor '(70 + -19b + -7b2)' equal to zero and attempt to solve:

Simplifying
70 + -19b + -7b2 = 0

Solving
70 + -19b + -7b2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-10 + 2.714285714b + b2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 2.714285714b + 10 + b2 = 0 + 10

Reorder the terms:
-10 + 10 + 2.714285714b + b2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 2.714285714b + b2 = 0 + 10
2.714285714b + b2 = 0 + 10

Combine like terms: 0 + 10 = 10
2.714285714b + b2 = 10

The b term is 2.714285714b.  Take half its coefficient (1.357142857).
Square it (1.841836734) and add it to both sides.

Add '1.841836734' to each side of the equation.
2.714285714b + 1.841836734 + b2 = 10 + 1.841836734

Reorder the terms:
1.841836734 + 2.714285714b + b2 = 10 + 1.841836734

Combine like terms: 10 + 1.841836734 = 11.841836734
1.841836734 + 2.714285714b + b2 = 11.841836734

Factor a perfect square on the left side:
(b + 1.357142857)(b + 1.357142857) = 11.841836734

Calculate the square root of the right side: 3.441196991

Break this problem into two subproblems by setting 
(b + 1.357142857) equal to 3.441196991 and -3.441196991.

Subproblem 1
b + 1.357142857 = 3.441196991

Simplifying
b + 1.357142857 = 3.441196991

Reorder the terms:
1.357142857 + b = 3.441196991

Solving
1.357142857 + b = 3.441196991

Solving for variable 'b'.

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

Add '-1.357142857' to each side of the equation.
1.357142857 + -1.357142857 + b = 3.441196991 + -1.357142857

Combine like terms: 1.357142857 + -1.357142857 = 0.000000000
0.000000000 + b = 3.441196991 + -1.357142857
b = 3.441196991 + -1.357142857

Combine like terms: 3.441196991 + -1.357142857 = 2.084054134
b = 2.084054134

Simplifying
b = 2.084054134

Subproblem 2
b + 1.357142857 = -3.441196991

Simplifying
b + 1.357142857 = -3.441196991

Reorder the terms:
1.357142857 + b = -3.441196991

Solving
1.357142857 + b = -3.441196991

Solving for variable 'b'.

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

Add '-1.357142857' to each side of the equation.
1.357142857 + -1.357142857 + b = -3.441196991 + -1.357142857

Combine like terms: 1.357142857 + -1.357142857 = 0.000000000
0.000000000 + b = -3.441196991 + -1.357142857
b = -3.441196991 + -1.357142857

Combine like terms: -3.441196991 + -1.357142857 = -4.798339848
b = -4.798339848

Simplifying
b = -4.798339848

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {2.084054134, -4.798339848}
Solution
b = {0, 2.084054134, -4.798339848}