2b^2=8b-6

Solution for 2b^2=8b-6 equation:

Simplifying
2b2 = 8b + -6

Reorder the terms:
2b2 = -6 + 8b

Solving
2b2 = -6 + 8b

Solving for variable 'b'.

Reorder the terms:
6 + -8b + 2b2 = -6 + 8b + 6 + -8b

Reorder the terms:
6 + -8b + 2b2 = -6 + 6 + 8b + -8b

Combine like terms: -6 + 6 = 0
6 + -8b + 2b2 = 0 + 8b + -8b
6 + -8b + 2b2 = 8b + -8b

Combine like terms: 8b + -8b = 0
6 + -8b + 2b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -4b + b2) = 0

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

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

Simplifying
1 + -1b = 0

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

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

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

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

Simplifying
b = 1
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 = {1, 3}