2b^2-3b=-1

Solution for 2b^2-3b=-1 equation:

Simplifying
2b2 + -3b = -1

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

Solving
-3b + 2b2 = -1

Solving for variable 'b'.

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

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

Factor a trinomial.
(1 + -2b)(1 + -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 '(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
Solution
b = {0.5, 1}