3b^2+9=6b+2b^2

Solution for 3b^2+9=6b+2b^2 equation:

Simplifying
3b2 + 9 = 6b + 2b2

Reorder the terms:
9 + 3b2 = 6b + 2b2

Solving
9 + 3b2 = 6b + 2b2

Solving for variable 'b'.

Reorder the terms:
9 + -6b + 3b2 + -2b2 = 6b + 2b2 + -6b + -2b2

Combine like terms: 3b2 + -2b2 = 1b2
9 + -6b + 1b2 = 6b + 2b2 + -6b + -2b2

Reorder the terms:
9 + -6b + 1b2 = 6b + -6b + 2b2 + -2b2

Combine like terms: 6b + -6b = 0
9 + -6b + 1b2 = 0 + 2b2 + -2b2
9 + -6b + 1b2 = 2b2 + -2b2

Combine like terms: 2b2 + -2b2 = 0
9 + -6b + 1b2 = 0

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

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 '(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 = {3, 3}