42b^2-43b-7=0

Solution for 42b^2-43b-7=0 equation:

Simplifying
42b2 + -43b + -7 = 0

Reorder the terms:
-7 + -43b + 42b2 = 0

Solving
-7 + -43b + 42b2 = 0

Solving for variable 'b'.

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

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

Simplifying
-1 + -7b = 0

Solving
-1 + -7b = 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 + -7b = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7b = 0 + 1
-7b = 0 + 1

Combine like terms: 0 + 1 = 1
-7b = 1

Divide each side by '-7'.
b = -0.1428571429

Simplifying
b = -0.1428571429
Subproblem 2
Set the factor '(7 + -6b)' equal to zero and attempt to solve:

Simplifying
7 + -6b = 0

Solving
7 + -6b = 0

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

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

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

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

Divide each side by '-6'.
b = 1.166666667

Simplifying
b = 1.166666667
Solution
b = {-0.1428571429, 1.166666667}