7k^2-42k=-63

Solution for 7k^2-42k=-63 equation:

Simplifying
7k2 + -42k = -63

Reorder the terms:
-42k + 7k2 = -63

Solving
-42k + 7k2 = -63

Solving for variable 'k'.

Reorder the terms:
63 + -42k + 7k2 = -63 + 63

Combine like terms: -63 + 63 = 0
63 + -42k + 7k2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(9 + -6k + k2) = 0

Factor a trinomial.
7((3 + -1k)(3 + -1k)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1k = 0 + -3

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

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

Divide each side by '-1'.
k = 3

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

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1k = 0 + -3

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

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

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Solution
k = {3, 3}