4b^2+3b-162=0

Solution for 4b^2+3b-162=0 equation:

Simplifying
4b2 + 3b + -162 = 0

Reorder the terms:
-162 + 3b + 4b2 = 0

Solving
-162 + 3b + 4b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-27 + -4b)(6 + -1b) = 0

Subproblem 1
Set the factor '(-27 + -4b)' equal to zero and attempt to solve:

Simplifying
-27 + -4b = 0

Solving
-27 + -4b = 0

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

Add '27' to each side of the equation.
-27 + 27 + -4b = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -4b = 0 + 27
-4b = 0 + 27

Combine like terms: 0 + 27 = 27
-4b = 27

Divide each side by '-4'.
b = -6.75

Simplifying
b = -6.75
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 = {-6.75, 6}