2b^2=30-b+b^2

Solution for 2b^2=30-b+b^2 equation:

Simplifying
2b2 = 30 + -1b + b2

Solving
2b2 = 30 + -1b + b2

Solving for variable 'b'.

Reorder the terms:
-30 + b + 2b2 + -1b2 = 30 + -1b + b2 + -30 + b + -1b2

Combine like terms: 2b2 + -1b2 = 1b2
-30 + b + 1b2 = 30 + -1b + b2 + -30 + b + -1b2

Reorder the terms:
-30 + b + 1b2 = 30 + -30 + -1b + b + b2 + -1b2

Combine like terms: 30 + -30 = 0
-30 + b + 1b2 = 0 + -1b + b + b2 + -1b2
-30 + b + 1b2 = -1b + b + b2 + -1b2

Combine like terms: -1b + b = 0
-30 + b + 1b2 = 0 + b2 + -1b2
-30 + b + 1b2 = b2 + -1b2

Combine like terms: b2 + -1b2 = 0
-30 + b + 1b2 = 0

Factor a trinomial.
(-6 + -1b)(5 + -1b) = 0

Subproblem 1
Set the factor '(-6 + -1b)' equal to zero and attempt to solve:

Simplifying
-6 + -1b = 0

Solving
-6 + -1b = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1b = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1b = 0 + 6
-1b = 0 + 6

Combine like terms: 0 + 6 = 6
-1b = 6

Divide each side by '-1'.
b = -6

Simplifying
b = -6
Subproblem 2
Set the factor '(5 + -1b)' equal to zero and attempt to solve:

Simplifying
5 + -1b = 0

Solving
5 + -1b = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1b = 0 + -5
-1b = 0 + -5

Combine like terms: 0 + -5 = -5
-1b = -5

Divide each side by '-1'.
b = 5

Simplifying
b = 5
Solution
b = {-6, 5}