7b^2-56b+105=0

Solution for 7b^2-56b+105=0 equation:

Simplifying
7b2 + -56b + 105 = 0

Reorder the terms:
105 + -56b + 7b2 = 0

Solving
105 + -56b + 7b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '7'.
7(15 + -8b + b2) = 0

Factor a trinomial.
7((3 + -1b)(5 + -1b)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Subproblem 2
Set the factor '(5 + -1b)' equal to zero and attempt to solve:

Simplifying
5 + -1b = 0

Solving
5 + -1b = 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 + -1b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1b = 0 + -5
-1b = 0 + -5

Combine like terms: 0 + -5 = -5
-1b = -5

Divide each side by '-1'.
b = 5

Simplifying
b = 5
Solution
b = {3, 5}