5b^2-4b=33

Solution for 5b^2-4b=33 equation:

Simplifying
5b2 + -4b = 33

Reorder the terms:
-4b + 5b2 = 33

Solving
-4b + 5b2 = 33

Solving for variable 'b'.

Reorder the terms:
-33 + -4b + 5b2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + -4b + 5b2 = 0

Factor a trinomial.
(-11 + -5b)(3 + -1b) = 0

Subproblem 1
Set the factor '(-11 + -5b)' equal to zero and attempt to solve:

Simplifying
-11 + -5b = 0

Solving
-11 + -5b = 0

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

Add '11' to each side of the equation.
-11 + 11 + -5b = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -5b = 0 + 11
-5b = 0 + 11

Combine like terms: 0 + 11 = 11
-5b = 11

Divide each side by '-5'.
b = -2.2

Simplifying
b = -2.2
Subproblem 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1b = 0 + -3

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

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

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {-2.2, 3}