3b^2=-2+7b

Solution for 3b^2=-2+7b equation:

Simplifying
3b2 = -2 + 7b

Solving
3b2 = -2 + 7b

Solving for variable 'b'.

Reorder the terms:
2 + -7b + 3b2 = -2 + 7b + 2 + -7b

Reorder the terms:
2 + -7b + 3b2 = -2 + 2 + 7b + -7b

Combine like terms: -2 + 2 = 0
2 + -7b + 3b2 = 0 + 7b + -7b
2 + -7b + 3b2 = 7b + -7b

Combine like terms: 7b + -7b = 0
2 + -7b + 3b2 = 0

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

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

Simplifying
1 + -3b = 0

Solving
1 + -3b = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3b = 0 + -1
-3b = 0 + -1

Combine like terms: 0 + -1 = -1
-3b = -1

Divide each side by '-3'.
b = 0.3333333333

Simplifying
b = 0.3333333333
Subproblem 2
Set the factor '(2 + -1b)' equal to zero and attempt to solve:

Simplifying
2 + -1b = 0

Solving
2 + -1b = 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 + -1b = 0 + -2

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

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

Divide each side by '-1'.
b = 2

Simplifying
b = 2
Solution
b = {0.3333333333, 2}