5(k+4)(k-8)=0

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Solution for 5(k+4)(k-8)=0 equation: 


Simplifying
5(k + 4)(k + -8) = 0

Reorder the terms:
5(4 + k)(k + -8) = 0

Reorder the terms:
5(4 + k)(-8 + k) = 0

Multiply (4 + k) * (-8 + k)
5(4(-8 + k) + k(-8 + k)) = 0
5((-8 * 4 + k * 4) + k(-8 + k)) = 0
5((-32 + 4k) + k(-8 + k)) = 0
5(-32 + 4k + (-8 * k + k * k)) = 0
5(-32 + 4k + (-8k + k2)) = 0

Combine like terms: 4k + -8k = -4k
5(-32 + -4k + k2) = 0
(-32 * 5 + -4k * 5 + k2 * 5) = 0
(-160 + -20k + 5k2) = 0

Solving
-160 + -20k + 5k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-32 + -4k + k2) = 0

Factor a trinomial.
5((-4 + -1k)(8 + -1k)) = 0

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
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
Solution
k = {-4, 8}

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