2k^2=-8k+64

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

Simplifying
2k2 = -8k + 64

Reorder the terms:
2k2 = 64 + -8k

Solving
2k2 = 64 + -8k

Solving for variable 'k'.

Reorder the terms:
-64 + 8k + 2k2 = 64 + -8k + -64 + 8k

Reorder the terms:
-64 + 8k + 2k2 = 64 + -64 + -8k + 8k

Combine like terms: 64 + -64 = 0
-64 + 8k + 2k2 = 0 + -8k + 8k
-64 + 8k + 2k2 = -8k + 8k

Combine like terms: -8k + 8k = 0
-64 + 8k + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + 4k + k2) = 0

Factor a trinomial.
2((-8 + -1k)(4 + -1k)) = 0

Ignore the factor 2.
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 '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Solution
k = {-8, 4}