7b(b+3)(b+4)+3b=

Solution for 7b(b+3)(b+4)+3b= equation:

Simplifying
7b(b + 3)(b + 4) + 3b = 0

Reorder the terms:
7b(3 + b)(b + 4) + 3b = 0

Reorder the terms:
7b(3 + b)(4 + b) + 3b = 0

Multiply (3 + b) * (4 + b)
7b(3(4 + b) + b(4 + b)) + 3b = 0
7b((4 * 3 + b * 3) + b(4 + b)) + 3b = 0
7b((12 + 3b) + b(4 + b)) + 3b = 0
7b(12 + 3b + (4 * b + b * b)) + 3b = 0
7b(12 + 3b + (4b + b2)) + 3b = 0

Combine like terms: 3b + 4b = 7b
7b(12 + 7b + b2) + 3b = 0
(12 * 7b + 7b * 7b + b2 * 7b) + 3b = 0
(84b + 49b2 + 7b3) + 3b = 0

Reorder the terms:
84b + 3b + 49b2 + 7b3 = 0

Combine like terms: 84b + 3b = 87b
87b + 49b2 + 7b3 = 0

Solving
87b + 49b2 + 7b3 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), 'b'.
b(87 + 49b + 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 '(87 + 49b + 7b2)' equal to zero and attempt to solve:

Simplifying
87 + 49b + 7b2 = 0

Solving
87 + 49b + 7b2 = 0

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

Divide each side by '7'.
12.42857143 + 7b + b2 = 0

Move the constant term to the right:

Add '-12.42857143' to each side of the equation.
12.42857143 + 7b + -12.42857143 + b2 = 0 + -12.42857143

Reorder the terms:
12.42857143 + -12.42857143 + 7b + b2 = 0 + -12.42857143

Combine like terms: 12.42857143 + -12.42857143 = 0.00000000
0.00000000 + 7b + b2 = 0 + -12.42857143
7b + b2 = 0 + -12.42857143

Combine like terms: 0 + -12.42857143 = -12.42857143
7b + b2 = -12.42857143

The b term is 7b.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7b + 12.25 + b2 = -12.42857143 + 12.25

Reorder the terms:
12.25 + 7b + b2 = -12.42857143 + 12.25

Combine like terms: -12.42857143 + 12.25 = -0.17857143
12.25 + 7b + b2 = -0.17857143

Factor a perfect square on the left side:
(b + 3.5)(b + 3.5) = -0.17857143

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
b = {0}