12b^2=32+40b

Solution for 12b^2=32+40b equation:

Simplifying
12b2 = 32 + 40b

Solving
12b2 = 32 + 40b

Solving for variable 'b'.

Reorder the terms:
-32 + -40b + 12b2 = 32 + 40b + -32 + -40b

Reorder the terms:
-32 + -40b + 12b2 = 32 + -32 + 40b + -40b

Combine like terms: 32 + -32 = 0
-32 + -40b + 12b2 = 0 + 40b + -40b
-32 + -40b + 12b2 = 40b + -40b

Combine like terms: 40b + -40b = 0
-32 + -40b + 12b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + -10b + 3b2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-2 + -3b)' equal to zero and attempt to solve:

Simplifying
-2 + -3b = 0

Solving
-2 + -3b = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3b = 0 + 2

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

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

Divide each side by '-3'.
b = -0.6666666667

Simplifying
b = -0.6666666667
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 = {-0.6666666667, 4}