6b^2+57b+126=0

Solution for 6b^2+57b+126=0 equation:

Simplifying
6b2 + 57b + 126 = 0

Reorder the terms:
126 + 57b + 6b2 = 0

Solving
126 + 57b + 6b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(42 + 19b + 2b2) = 0

Factor a trinomial.
3((6 + b)(7 + 2b)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + b)' equal to zero and attempt to solve:

Simplifying
6 + b = 0

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

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

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

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

Simplifying
7 + 2b = 0

Solving
7 + 2b = 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 + 2b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2b = 0 + -7
2b = 0 + -7

Combine like terms: 0 + -7 = -7
2b = -7

Divide each side by '2'.
b = -3.5

Simplifying
b = -3.5
Solution
b = {-6, -3.5}