7b^2-42b+56=0

Solution for 7b^2-42b+56=0 equation:

Simplifying
7b2 + -42b + 56 = 0

Reorder the terms:
56 + -42b + 7b2 = 0

Solving
56 + -42b + 7b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '7'.
7(8 + -6b + b2) = 0

Factor a trinomial.
7((2 + -1b)(4 + -1b)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(2 + -1b)' equal to zero and attempt to solve:

Simplifying
2 + -1b = 0

Solving
2 + -1b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1b = 0 + -2
-1b = 0 + -2

Combine like terms: 0 + -2 = -2
-1b = -2

Divide each side by '-1'.
b = 2

Simplifying
b = 2
Subproblem 2
Set the factor '(4 + -1b)' equal to zero and attempt to solve:

Simplifying
4 + -1b = 0

Solving
4 + -1b = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1b = 0 + -4
-1b = 0 + -4

Combine like terms: 0 + -4 = -4
-1b = -4

Divide each side by '-1'.
b = 4

Simplifying
b = 4
Solution
b = {2, 4}