-5k^2+6k=1

Solution for -5k^2+6k=1 equation:

Simplifying
-5k2 + 6k = 1

Reorder the terms:
6k + -5k2 = 1

Solving
6k + -5k2 = 1

Solving for variable 'k'.

Reorder the terms:
-1 + 6k + -5k2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 6k + -5k2 = 0

Factor a trinomial.
(-1 + k)(1 + -5k) = 0

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

Simplifying
-1 + k = 0

Solving
-1 + k = 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 + k = 0 + 1

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

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

Simplifying
k = 1
Subproblem 2
Set the factor '(1 + -5k)' equal to zero and attempt to solve:

Simplifying
1 + -5k = 0

Solving
1 + -5k = 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 + -5k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5k = 0 + -1
-5k = 0 + -1

Combine like terms: 0 + -1 = -1
-5k = -1

Divide each side by '-5'.
k = 0.2

Simplifying
k = 0.2
Solution
k = {1, 0.2}