1b^2+3b=54

Solution for 1b^2+3b=54 equation:

Simplifying
1b2 + 3b = 54

Reorder the terms:
3b + 1b2 = 54

Solving
3b + 1b2 = 54

Solving for variable 'b'.

Reorder the terms:
-54 + 3b + 1b2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + 3b + 1b2 = 0

Factor a trinomial.
(-9 + -1b)(6 + -1b) = 0

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

Simplifying
-9 + -1b = 0

Solving
-9 + -1b = 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 + -1b = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1b = 0 + 9
-1b = 0 + 9

Combine like terms: 0 + 9 = 9
-1b = 9

Divide each side by '-1'.
b = -9

Simplifying
b = -9
Subproblem 2
Set the factor '(6 + -1b)' equal to zero and attempt to solve:

Simplifying
6 + -1b = 0

Solving
6 + -1b = 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 + -1b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1b = 0 + -6
-1b = 0 + -6

Combine like terms: 0 + -6 = -6
-1b = -6

Divide each side by '-1'.
b = 6

Simplifying
b = 6
Solution
b = {-9, 6}