2b^2=90-8b

Solution for 2b^2=90-8b equation:

Simplifying
2b2 = 90 + -8b

Solving
2b2 = 90 + -8b

Solving for variable 'b'.

Reorder the terms:
-90 + 8b + 2b2 = 90 + -8b + -90 + 8b

Reorder the terms:
-90 + 8b + 2b2 = 90 + -90 + -8b + 8b

Combine like terms: 90 + -90 = 0
-90 + 8b + 2b2 = 0 + -8b + 8b
-90 + 8b + 2b2 = -8b + 8b

Combine like terms: -8b + 8b = 0
-90 + 8b + 2b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 4b + b2) = 0

Factor a trinomial.
2((-9 + -1b)(5 + -1b)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -1b)' equal to zero and attempt to solve:

Simplifying
-9 + -1b = 0

Solving
-9 + -1b = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1b = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1b = 0 + 9
-1b = 0 + 9

Combine like terms: 0 + 9 = 9
-1b = 9

Divide each side by '-1'.
b = -9

Simplifying
b = -9
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 = {-9, 5}