3b^2+45b+78=0

Solution for 3b^2+45b+78=0 equation:

Simplifying
3b2 + 45b + 78 = 0

Reorder the terms:
78 + 45b + 3b2 = 0

Solving
78 + 45b + 3b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(26 + 15b + b2) = 0

Factor a trinomial.
3((13 + b)(2 + b)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(13 + b)' equal to zero and attempt to solve:

Simplifying
13 + b = 0

Solving
13 + b = 0

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

Add '-13' to each side of the equation.
13 + -13 + b = 0 + -13

Combine like terms: 13 + -13 = 0
0 + b = 0 + -13
b = 0 + -13

Combine like terms: 0 + -13 = -13
b = -13

Simplifying
b = -13
Subproblem 2
Set the factor '(2 + b)' equal to zero and attempt to solve:

Simplifying
2 + b = 0

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

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

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

Simplifying
b = -2
Solution
b = {-13, -2}