8(k+4)+(k+3)(k+4)=5(k+3)

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Solution for 8(k+4)+(k+3)(k+4)=5(k+3) equation: 


Simplifying
8(k + 4) + (k + 3)(k + 4) = 5(k + 3)

Reorder the terms:
8(4 + k) + (k + 3)(k + 4) = 5(k + 3)
(4 * 8 + k * 8) + (k + 3)(k + 4) = 5(k + 3)
(32 + 8k) + (k + 3)(k + 4) = 5(k + 3)

Reorder the terms:
32 + 8k + (3 + k)(k + 4) = 5(k + 3)

Reorder the terms:
32 + 8k + (3 + k)(4 + k) = 5(k + 3)

Multiply (3 + k) * (4 + k)
32 + 8k + (3(4 + k) + k(4 + k)) = 5(k + 3)
32 + 8k + ((4 * 3 + k * 3) + k(4 + k)) = 5(k + 3)
32 + 8k + ((12 + 3k) + k(4 + k)) = 5(k + 3)
32 + 8k + (12 + 3k + (4 * k + k * k)) = 5(k + 3)
32 + 8k + (12 + 3k + (4k + k2)) = 5(k + 3)

Combine like terms: 3k + 4k = 7k
32 + 8k + (12 + 7k + k2) = 5(k + 3)

Reorder the terms:
32 + 12 + 8k + 7k + k2 = 5(k + 3)

Combine like terms: 32 + 12 = 44
44 + 8k + 7k + k2 = 5(k + 3)

Combine like terms: 8k + 7k = 15k
44 + 15k + k2 = 5(k + 3)

Reorder the terms:
44 + 15k + k2 = 5(3 + k)
44 + 15k + k2 = (3 * 5 + k * 5)
44 + 15k + k2 = (15 + 5k)

Solving
44 + 15k + k2 = 15 + 5k

Solving for variable 'k'.

Reorder the terms:
44 + -15 + 15k + -5k + k2 = 15 + 5k + -15 + -5k

Combine like terms: 44 + -15 = 29
29 + 15k + -5k + k2 = 15 + 5k + -15 + -5k

Combine like terms: 15k + -5k = 10k
29 + 10k + k2 = 15 + 5k + -15 + -5k

Reorder the terms:
29 + 10k + k2 = 15 + -15 + 5k + -5k

Combine like terms: 15 + -15 = 0
29 + 10k + k2 = 0 + 5k + -5k
29 + 10k + k2 = 5k + -5k

Combine like terms: 5k + -5k = 0
29 + 10k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-29' to each side of the equation.
29 + 10k + -29 + k2 = 0 + -29

Reorder the terms:
29 + -29 + 10k + k2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + 10k + k2 = 0 + -29
10k + k2 = 0 + -29

Combine like terms: 0 + -29 = -29
10k + k2 = -29

The k term is 10k.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10k + 25 + k2 = -29 + 25

Reorder the terms:
25 + 10k + k2 = -29 + 25

Combine like terms: -29 + 25 = -4
25 + 10k + k2 = -4

Factor a perfect square on the left side:
(k + 5)(k + 5) = -4

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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