24=2b^2+2b

Solution for 24=2b^2+2b equation:

Simplifying
24 = 2b2 + 2b

Reorder the terms:
24 = 2b + 2b2

Solving
24 = 2b + 2b2

Solving for variable 'b'.

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

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

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

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

Factor a trinomial.
2((3 + -1b)(4 + b)) = 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 + b)' equal to zero and attempt to solve:

Simplifying
4 + b = 0

Solving
4 + b = 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 + b = 0 + -4

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

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

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