2b^2-6b=b-3

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

Simplifying
2b2 + -6b = b + -3

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

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

Solving
-6b + 2b2 = -3 + b

Solving for variable 'b'.

Reorder the terms:
3 + -6b + -1b + 2b2 = -3 + b + 3 + -1b

Combine like terms: -6b + -1b = -7b
3 + -7b + 2b2 = -3 + b + 3 + -1b

Reorder the terms:
3 + -7b + 2b2 = -3 + 3 + b + -1b

Combine like terms: -3 + 3 = 0
3 + -7b + 2b2 = 0 + b + -1b
3 + -7b + 2b2 = b + -1b

Combine like terms: b + -1b = 0
3 + -7b + 2b2 = 0

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

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

Simplifying
1 + -2b = 0

Solving
1 + -2b = 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 + -2b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2b = 0 + -1
-2b = 0 + -1

Combine like terms: 0 + -1 = -1
-2b = -1

Divide each side by '-2'.
b = 0.5

Simplifying
b = 0.5
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 = {0.5, 3}