4(k-8)(k-8)=16

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Solution for 4(k-8)(k-8)=16 equation: 


Simplifying
4(k + -8)(k + -8) = 16

Reorder the terms:
4(-8 + k)(k + -8) = 16

Reorder the terms:
4(-8 + k)(-8 + k) = 16

Multiply (-8 + k) * (-8 + k)
4(-8(-8 + k) + k(-8 + k)) = 16
4((-8 * -8 + k * -8) + k(-8 + k)) = 16
4((64 + -8k) + k(-8 + k)) = 16
4(64 + -8k + (-8 * k + k * k)) = 16
4(64 + -8k + (-8k + k2)) = 16

Combine like terms: -8k + -8k = -16k
4(64 + -16k + k2) = 16
(64 * 4 + -16k * 4 + k2 * 4) = 16
(256 + -64k + 4k2) = 16

Solving
256 + -64k + 4k2 = 16

Solving for variable 'k'.

Reorder the terms:
256 + -16 + -64k + 4k2 = 16 + -16

Combine like terms: 256 + -16 = 240
240 + -64k + 4k2 = 16 + -16

Combine like terms: 16 + -16 = 0
240 + -64k + 4k2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(60 + -16k + k2) = 0

Factor a trinomial.
4((6 + -1k)(10 + -1k)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(6 + -1k)' equal to zero and attempt to solve:

Simplifying
6 + -1k = 0

Solving
6 + -1k = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1k = 0 + -6

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

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

Divide each side by '-1'.
k = 6

Simplifying
k = 6

Subproblem 2
Set the factor '(10 + -1k)' equal to zero and attempt to solve:

Simplifying
10 + -1k = 0

Solving
10 + -1k = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1k = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1k = 0 + -10
-1k = 0 + -10

Combine like terms: 0 + -10 = -10
-1k = -10

Divide each side by '-1'.
k = 10

Simplifying
k = 10
Solution
k = {6, 10}

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