(18b^2+6b-7)-(-3b^2+5b+8)=

Solution for (18b^2+6b-7)-(-3b^2+5b+8)= equation:

Simplifying
(18b2 + 6b + -7) + -1(-3b2 + 5b + 8) = 0

Reorder the terms:
(-7 + 6b + 18b2) + -1(-3b2 + 5b + 8) = 0

Remove parenthesis around (-7 + 6b + 18b2)
-7 + 6b + 18b2 + -1(-3b2 + 5b + 8) = 0

Reorder the terms:
-7 + 6b + 18b2 + -1(8 + 5b + -3b2) = 0
-7 + 6b + 18b2 + (8 * -1 + 5b * -1 + -3b2 * -1) = 0
-7 + 6b + 18b2 + (-8 + -5b + 3b2) = 0

Reorder the terms:
-7 + -8 + 6b + -5b + 18b2 + 3b2 = 0

Combine like terms: -7 + -8 = -15
-15 + 6b + -5b + 18b2 + 3b2 = 0

Combine like terms: 6b + -5b = 1b
-15 + 1b + 18b2 + 3b2 = 0

Combine like terms: 18b2 + 3b2 = 21b2
-15 + 1b + 21b2 = 0

Solving
-15 + 1b + 21b2 = 0

Solving for variable 'b'.

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

Divide each side by '21'.
-0.7142857143 + 0.04761904762b + b2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + 0.04761904762b + 0.7142857143 + b2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + 0.04761904762b + b2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + 0.04761904762b + b2 = 0 + 0.7142857143
0.04761904762b + b2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
0.04761904762b + b2 = 0.7142857143

The b term is 0.04761904762b.  Take half its coefficient (0.02380952381).
Square it (0.0005668934241) and add it to both sides.

Add '0.0005668934241' to each side of the equation.
0.04761904762b + 0.0005668934241 + b2 = 0.7142857143 + 0.0005668934241

Reorder the terms:
0.0005668934241 + 0.04761904762b + b2 = 0.7142857143 + 0.0005668934241

Combine like terms: 0.7142857143 + 0.0005668934241 = 0.7148526077241
0.0005668934241 + 0.04761904762b + b2 = 0.7148526077241

Factor a perfect square on the left side:
(b + 0.02380952381)(b + 0.02380952381) = 0.7148526077241

Calculate the square root of the right side: 0.845489567

Break this problem into two subproblems by setting 
(b + 0.02380952381) equal to 0.845489567 and -0.845489567.

Subproblem 1
b + 0.02380952381 = 0.845489567

Simplifying
b + 0.02380952381 = 0.845489567

Reorder the terms:
0.02380952381 + b = 0.845489567

Solving
0.02380952381 + b = 0.845489567

Solving for variable 'b'.

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

Add '-0.02380952381' to each side of the equation.
0.02380952381 + -0.02380952381 + b = 0.845489567 + -0.02380952381

Combine like terms: 0.02380952381 + -0.02380952381 = 0.00000000000
0.00000000000 + b = 0.845489567 + -0.02380952381
b = 0.845489567 + -0.02380952381

Combine like terms: 0.845489567 + -0.02380952381 = 0.82168004319
b = 0.82168004319

Simplifying
b = 0.82168004319

Subproblem 2
b + 0.02380952381 = -0.845489567

Simplifying
b + 0.02380952381 = -0.845489567

Reorder the terms:
0.02380952381 + b = -0.845489567

Solving
0.02380952381 + b = -0.845489567

Solving for variable 'b'.

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

Add '-0.02380952381' to each side of the equation.
0.02380952381 + -0.02380952381 + b = -0.845489567 + -0.02380952381

Combine like terms: 0.02380952381 + -0.02380952381 = 0.00000000000
0.00000000000 + b = -0.845489567 + -0.02380952381
b = -0.845489567 + -0.02380952381

Combine like terms: -0.845489567 + -0.02380952381 = -0.86929909081
b = -0.86929909081

Simplifying
b = -0.86929909081

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.82168004319, -0.86929909081}