7b^2+35=5-41b

Solution for 7b^2+35=5-41b equation:

Simplifying
7b2 + 35 = 5 + -41b

Reorder the terms:
35 + 7b2 = 5 + -41b

Solving
35 + 7b2 = 5 + -41b

Solving for variable 'b'.

Reorder the terms:
35 + -5 + 41b + 7b2 = 5 + -41b + -5 + 41b

Combine like terms: 35 + -5 = 30
30 + 41b + 7b2 = 5 + -41b + -5 + 41b

Reorder the terms:
30 + 41b + 7b2 = 5 + -5 + -41b + 41b

Combine like terms: 5 + -5 = 0
30 + 41b + 7b2 = 0 + -41b + 41b
30 + 41b + 7b2 = -41b + 41b

Combine like terms: -41b + 41b = 0
30 + 41b + 7b2 = 0

Factor a trinomial.
(5 + b)(6 + 7b) = 0

Subproblem 1
Set the factor '(5 + b)' equal to zero and attempt to solve:

Simplifying
5 + b = 0

Solving
5 + b = 0

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

Add '-5' to each side of the equation.
5 + -5 + b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + b = 0 + -5
b = 0 + -5

Combine like terms: 0 + -5 = -5
b = -5

Simplifying
b = -5
Subproblem 2
Set the factor '(6 + 7b)' equal to zero and attempt to solve:

Simplifying
6 + 7b = 0

Solving
6 + 7b = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7b = 0 + -6
7b = 0 + -6

Combine like terms: 0 + -6 = -6
7b = -6

Divide each side by '7'.
b = -0.8571428571

Simplifying
b = -0.8571428571
Solution
b = {-5, -0.8571428571}