8k^2-64=-56k

Solution for 8k^2-64=-56k equation:

Simplifying
8k2 + -64 = -56k

Reorder the terms:
-64 + 8k2 = -56k

Solving
-64 + 8k2 = -56k

Solving for variable 'k'.

Reorder the terms:
-64 + 56k + 8k2 = -56k + 56k

Combine like terms: -56k + 56k = 0
-64 + 56k + 8k2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-8 + 7k + k2) = 0

Factor a trinomial.
8((-8 + -1k)(1 + -1k)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-8 + -1k)' equal to zero and attempt to solve:

Simplifying
-8 + -1k = 0

Solving
-8 + -1k = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1k = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1k = 0 + 8
-1k = 0 + 8

Combine like terms: 0 + 8 = 8
-1k = 8

Divide each side by '-1'.
k = -8

Simplifying
k = -8
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 = {-8, 1}