23k=5k-8-7k^2

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Solution for 23k=5k-8-7k^2 equation: 


Simplifying
23k = 5k + -8 + -7k2

Reorder the terms:
23k = -8 + 5k + -7k2

Solving
23k = -8 + 5k + -7k2

Solving for variable 'k'.

Reorder the terms:
8 + 23k + -5k + 7k2 = -8 + 5k + -7k2 + 8 + -5k + 7k2

Combine like terms: 23k + -5k = 18k
8 + 18k + 7k2 = -8 + 5k + -7k2 + 8 + -5k + 7k2

Reorder the terms:
8 + 18k + 7k2 = -8 + 8 + 5k + -5k + -7k2 + 7k2

Combine like terms: -8 + 8 = 0
8 + 18k + 7k2 = 0 + 5k + -5k + -7k2 + 7k2
8 + 18k + 7k2 = 5k + -5k + -7k2 + 7k2

Combine like terms: 5k + -5k = 0
8 + 18k + 7k2 = 0 + -7k2 + 7k2
8 + 18k + 7k2 = -7k2 + 7k2

Combine like terms: -7k2 + 7k2 = 0
8 + 18k + 7k2 = 0

Factor a trinomial.
(2 + k)(4 + 7k) = 0


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

Simplifying
2 + k = 0

Solving
2 + k = 0

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

Add '-2' to each side of the equation.
2 + -2 + k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + k = 0 + -2
k = 0 + -2

Combine like terms: 0 + -2 = -2
k = -2

Simplifying
k = -2

Subproblem 2
Set the factor '(4 + 7k)' equal to zero and attempt to solve:

Simplifying
4 + 7k = 0

Solving
4 + 7k = 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 + 7k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7k = 0 + -4
7k = 0 + -4

Combine like terms: 0 + -4 = -4
7k = -4

Divide each side by '7'.
k = -0.5714285714

Simplifying
k = -0.5714285714
Solution
k = {-2, -0.5714285714}

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