12-4b=7b-2b^2

Solution for 12-4b=7b-2b^2 equation:

Simplifying
12 + -4b = 7b + -2b2

Solving
12 + -4b = 7b + -2b2

Solving for variable 'b'.

Combine like terms: -4b + -7b = -11b
12 + -11b + 2b2 = 7b + -2b2 + -7b + 2b2

Reorder the terms:
12 + -11b + 2b2 = 7b + -7b + -2b2 + 2b2

Combine like terms: 7b + -7b = 0
12 + -11b + 2b2 = 0 + -2b2 + 2b2
12 + -11b + 2b2 = -2b2 + 2b2

Combine like terms: -2b2 + 2b2 = 0
12 + -11b + 2b2 = 0

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

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

Simplifying
3 + -2b = 0

Solving
3 + -2b = 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 + -2b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2b = 0 + -3
-2b = 0 + -3

Combine like terms: 0 + -3 = -3
-2b = -3

Divide each side by '-2'.
b = 1.5

Simplifying
b = 1.5
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 = {1.5, 4}