6b^2+47b+90=0

Solution for 6b^2+47b+90=0 equation:

Simplifying
6b2 + 47b + 90 = 0

Reorder the terms:
90 + 47b + 6b2 = 0

Solving
90 + 47b + 6b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(9 + 2b)(10 + 3b) = 0

Subproblem 1
Set the factor '(9 + 2b)' equal to zero and attempt to solve:

Simplifying
9 + 2b = 0

Solving
9 + 2b = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2b = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2b = 0 + -9
2b = 0 + -9

Combine like terms: 0 + -9 = -9
2b = -9

Divide each side by '2'.
b = -4.5

Simplifying
b = -4.5
Subproblem 2
Set the factor '(10 + 3b)' equal to zero and attempt to solve:

Simplifying
10 + 3b = 0

Solving
10 + 3b = 0

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

Add '-10' to each side of the equation.
10 + -10 + 3b = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3b = 0 + -10
3b = 0 + -10

Combine like terms: 0 + -10 = -10
3b = -10

Divide each side by '3'.
b = -3.333333333

Simplifying
b = -3.333333333
Solution
b = {-4.5, -3.333333333}