42b^2+300b+42=0

Solution for 42b^2+300b+42=0 equation:

Simplifying
42b2 + 300b + 42 = 0

Reorder the terms:
42 + 300b + 42b2 = 0

Solving
42 + 300b + 42b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '6'.
6(7 + 50b + 7b2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(7 + b)' equal to zero and attempt to solve:

Simplifying
7 + b = 0

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

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

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

Simplifying
b = -7
Subproblem 2
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
Solution
b = {-7, -0.1428571429}