3b^2-6=7b

Solution for 3b^2-6=7b equation:

Simplifying
3b2 + -6 = 7b

Reorder the terms:
-6 + 3b2 = 7b

Solving
-6 + 3b2 = 7b

Solving for variable 'b'.

Reorder the terms:
-6 + -7b + 3b2 = 7b + -7b

Combine like terms: 7b + -7b = 0
-6 + -7b + 3b2 = 0

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

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 '(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
Solution
b = {-0.6666666667, 3}