8(k-46)(k+23)=0

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Solution for 8(k-46)(k+23)=0 equation: 


Simplifying
8(k + -46)(k + 23) = 0

Reorder the terms:
8(-46 + k)(k + 23) = 0

Reorder the terms:
8(-46 + k)(23 + k) = 0

Multiply (-46 + k) * (23 + k)
8(-46(23 + k) + k(23 + k)) = 0
8((23 * -46 + k * -46) + k(23 + k)) = 0
8((-1058 + -46k) + k(23 + k)) = 0
8(-1058 + -46k + (23 * k + k * k)) = 0
8(-1058 + -46k + (23k + k2)) = 0

Combine like terms: -46k + 23k = -23k
8(-1058 + -23k + k2) = 0
(-1058 * 8 + -23k * 8 + k2 * 8) = 0
(-8464 + -184k + 8k2) = 0

Solving
-8464 + -184k + 8k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-1058 + -23k + k2) = 0

Factor a trinomial.
8((-23 + -1k)(46 + -1k)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-23 + -1k)' equal to zero and attempt to solve:

Simplifying
-23 + -1k = 0

Solving
-23 + -1k = 0

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

Add '23' to each side of the equation.
-23 + 23 + -1k = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -1k = 0 + 23
-1k = 0 + 23

Combine like terms: 0 + 23 = 23
-1k = 23

Divide each side by '-1'.
k = -23

Simplifying
k = -23

Subproblem 2
Set the factor '(46 + -1k)' equal to zero and attempt to solve:

Simplifying
46 + -1k = 0

Solving
46 + -1k = 0

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

Add '-46' to each side of the equation.
46 + -46 + -1k = 0 + -46

Combine like terms: 46 + -46 = 0
0 + -1k = 0 + -46
-1k = 0 + -46

Combine like terms: 0 + -46 = -46
-1k = -46

Divide each side by '-1'.
k = 46

Simplifying
k = 46
Solution
k = {-23, 46}

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