2k^2-3k=-1

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

Simplifying
2k2 + -3k = -1

Reorder the terms:
-3k + 2k2 = -1

Solving
-3k + 2k2 = -1

Solving for variable 'k'.

Reorder the terms:
1 + -3k + 2k2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -3k + 2k2 = 0

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

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

Simplifying
1 + -2k = 0

Solving
1 + -2k = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2k = 0 + -1

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

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

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

Simplifying
k = 0.5
Subproblem 2
Set the factor '(1 + -1k)' equal to zero and attempt to solve:

Simplifying
1 + -1k = 0

Solving
1 + -1k = 0

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

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

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

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

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

Simplifying
k = 1
Solution
k = {0.5, 1}