2b^2-3b-24=-b

Solution for 2b^2-3b-24=-b equation:

Simplifying
2b2 + -3b + -24 = -1b

Reorder the terms:
-24 + -3b + 2b2 = -1b

Solving
-24 + -3b + 2b2 = -1b

Solving for variable 'b'.

Reorder the terms:
-24 + -3b + b + 2b2 = -1b + b

Combine like terms: -3b + b = -2b
-24 + -2b + 2b2 = -1b + b

Combine like terms: -1b + b = 0
-24 + -2b + 2b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -1b + b2) = 0

Factor a trinomial.
2((-3 + -1b)(4 + -1b)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1b)' equal to zero and attempt to solve:

Simplifying
4 + -1b = 0

Solving
4 + -1b = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1b = 0 + -4
-1b = 0 + -4

Combine like terms: 0 + -4 = -4
-1b = -4

Divide each side by '-1'.
b = 4

Simplifying
b = 4
Solution
b = {-3, 4}