3k^2-3k+1=7

Solution for 3k^2-3k+1=7 equation:

Simplifying
3k2 + -3k + 1 = 7

Reorder the terms:
1 + -3k + 3k2 = 7

Solving
1 + -3k + 3k2 = 7

Solving for variable 'k'.

Reorder the terms:
1 + -7 + -3k + 3k2 = 7 + -7

Combine like terms: 1 + -7 = -6
-6 + -3k + 3k2 = 7 + -7

Combine like terms: 7 + -7 = 0
-6 + -3k + 3k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -1k + k2) = 0

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

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

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

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

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

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

Divide each side by '-1'.
k = 2

Simplifying
k = 2
Solution
k = {-1, 2}