(6b^4+6b^3-13b^2)-(3b^3+9b^2-8b^4)=

Solution for (6b^4+6b^3-13b^2)-(3b^3+9b^2-8b^4)= equation:

Simplifying
(6b4 + 6b3 + -13b2) + -1(3b3 + 9b2 + -8b4) = 0

Reorder the terms:
(-13b2 + 6b3 + 6b4) + -1(3b3 + 9b2 + -8b4) = 0

Remove parenthesis around (-13b2 + 6b3 + 6b4)
-13b2 + 6b3 + 6b4 + -1(3b3 + 9b2 + -8b4) = 0

Reorder the terms:
-13b2 + 6b3 + 6b4 + -1(9b2 + 3b3 + -8b4) = 0
-13b2 + 6b3 + 6b4 + (9b2 * -1 + 3b3 * -1 + -8b4 * -1) = 0
-13b2 + 6b3 + 6b4 + (-9b2 + -3b3 + 8b4) = 0

Reorder the terms:
-13b2 + -9b2 + 6b3 + -3b3 + 6b4 + 8b4 = 0

Combine like terms: -13b2 + -9b2 = -22b2
-22b2 + 6b3 + -3b3 + 6b4 + 8b4 = 0

Combine like terms: 6b3 + -3b3 = 3b3
-22b2 + 3b3 + 6b4 + 8b4 = 0

Combine like terms: 6b4 + 8b4 = 14b4
-22b2 + 3b3 + 14b4 = 0

Solving
-22b2 + 3b3 + 14b4 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), 'b2'.
b2(-22 + 3b + 14b2) = 0

Subproblem 1
Set the factor 'b2' equal to zero and attempt to solve:

Simplifying
b2 = 0

Solving
b2 = 0

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

Simplifying
b2 = 0

Take the square root of each side:
b = {0}
Subproblem 2
Set the factor '(-22 + 3b + 14b2)' equal to zero and attempt to solve:

Simplifying
-22 + 3b + 14b2 = 0

Solving
-22 + 3b + 14b2 = 0

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

Divide each side by '14'.
-1.571428571 + 0.2142857143b + b2 = 0

Move the constant term to the right:

Add '1.571428571' to each side of the equation.
-1.571428571 + 0.2142857143b + 1.571428571 + b2 = 0 + 1.571428571

Reorder the terms:
-1.571428571 + 1.571428571 + 0.2142857143b + b2 = 0 + 1.571428571

Combine like terms: -1.571428571 + 1.571428571 = 0.000000000
0.000000000 + 0.2142857143b + b2 = 0 + 1.571428571
0.2142857143b + b2 = 0 + 1.571428571

Combine like terms: 0 + 1.571428571 = 1.571428571
0.2142857143b + b2 = 1.571428571

The b term is 0.2142857143b.  Take half its coefficient (0.1071428572).
Square it (0.01147959185) and add it to both sides.

Add '0.01147959185' to each side of the equation.
0.2142857143b + 0.01147959185 + b2 = 1.571428571 + 0.01147959185

Reorder the terms:
0.01147959185 + 0.2142857143b + b2 = 1.571428571 + 0.01147959185

Combine like terms: 1.571428571 + 0.01147959185 = 1.58290816285
0.01147959185 + 0.2142857143b + b2 = 1.58290816285

Factor a perfect square on the left side:
(b + 0.1071428572)(b + 0.1071428572) = 1.58290816285

Calculate the square root of the right side: 1.258136782

Break this problem into two subproblems by setting 
(b + 0.1071428572) equal to 1.258136782 and -1.258136782.

Subproblem 1
b + 0.1071428572 = 1.258136782

Simplifying
b + 0.1071428572 = 1.258136782

Reorder the terms:
0.1071428572 + b = 1.258136782

Solving
0.1071428572 + b = 1.258136782

Solving for variable 'b'.

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

Add '-0.1071428572' to each side of the equation.
0.1071428572 + -0.1071428572 + b = 1.258136782 + -0.1071428572

Combine like terms: 0.1071428572 + -0.1071428572 = 0.0000000000
0.0000000000 + b = 1.258136782 + -0.1071428572
b = 1.258136782 + -0.1071428572

Combine like terms: 1.258136782 + -0.1071428572 = 1.1509939248
b = 1.1509939248

Simplifying
b = 1.1509939248

Subproblem 2
b + 0.1071428572 = -1.258136782

Simplifying
b + 0.1071428572 = -1.258136782

Reorder the terms:
0.1071428572 + b = -1.258136782

Solving
0.1071428572 + b = -1.258136782

Solving for variable 'b'.

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

Add '-0.1071428572' to each side of the equation.
0.1071428572 + -0.1071428572 + b = -1.258136782 + -0.1071428572

Combine like terms: 0.1071428572 + -0.1071428572 = 0.0000000000
0.0000000000 + b = -1.258136782 + -0.1071428572
b = -1.258136782 + -0.1071428572

Combine like terms: -1.258136782 + -0.1071428572 = -1.3652796392
b = -1.3652796392

Simplifying
b = -1.3652796392

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.1509939248, -1.3652796392}
Solution
b = {0, 1.1509939248, -1.3652796392}