7b^2-49b=-42

Solution for 7b^2-49b=-42 equation:

Simplifying
7b2 + -49b = -42

Reorder the terms:
-49b + 7b2 = -42

Solving
-49b + 7b2 = -42

Solving for variable 'b'.

Reorder the terms:
42 + -49b + 7b2 = -42 + 42

Combine like terms: -42 + 42 = 0
42 + -49b + 7b2 = 0

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

Factor a trinomial.
7((1 + -1b)(6 + -1b)) = 0

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

Simplifying
1 + -1b = 0

Solving
1 + -1b = 0

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

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

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

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

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

Simplifying
b = 1
Subproblem 2
Set the factor '(6 + -1b)' equal to zero and attempt to solve:

Simplifying
6 + -1b = 0

Solving
6 + -1b = 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 + -1b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1b = 0 + -6
-1b = 0 + -6

Combine like terms: 0 + -6 = -6
-1b = -6

Divide each side by '-1'.
b = 6

Simplifying
b = 6
Solution
b = {1, 6}