2b^2+5b-22=11

Solution for 2b^2+5b-22=11 equation:

Simplifying
2b2 + 5b + -22 = 11

Reorder the terms:
-22 + 5b + 2b2 = 11

Solving
-22 + 5b + 2b2 = 11

Solving for variable 'b'.

Reorder the terms:
-22 + -11 + 5b + 2b2 = 11 + -11

Combine like terms: -22 + -11 = -33
-33 + 5b + 2b2 = 11 + -11

Combine like terms: 11 + -11 = 0
-33 + 5b + 2b2 = 0

Factor a trinomial.
(-11 + -2b)(3 + -1b) = 0

Subproblem 1
Set the factor '(-11 + -2b)' equal to zero and attempt to solve:

Simplifying
-11 + -2b = 0

Solving
-11 + -2b = 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 + -2b = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2b = 0 + 11
-2b = 0 + 11

Combine like terms: 0 + 11 = 11
-2b = 11

Divide each side by '-2'.
b = -5.5

Simplifying
b = -5.5
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 = {-5.5, 3}