4(k+2)-8k-5=-3k+9-2k(k+6)

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Solution for 4(k+2)-8k-5=-3k+9-2k(k+6) equation: 


Simplifying
4(k + 2) + -8k + -5 = -3k + 9 + -2k(k + 6)

Reorder the terms:
4(2 + k) + -8k + -5 = -3k + 9 + -2k(k + 6)
(2 * 4 + k * 4) + -8k + -5 = -3k + 9 + -2k(k + 6)
(8 + 4k) + -8k + -5 = -3k + 9 + -2k(k + 6)

Reorder the terms:
8 + -5 + 4k + -8k = -3k + 9 + -2k(k + 6)

Combine like terms: 8 + -5 = 3
3 + 4k + -8k = -3k + 9 + -2k(k + 6)

Combine like terms: 4k + -8k = -4k
3 + -4k = -3k + 9 + -2k(k + 6)

Reorder the terms:
3 + -4k = -3k + 9 + -2k(6 + k)
3 + -4k = -3k + 9 + (6 * -2k + k * -2k)
3 + -4k = -3k + 9 + (-12k + -2k2)

Reorder the terms:
3 + -4k = 9 + -3k + -12k + -2k2

Combine like terms: -3k + -12k = -15k
3 + -4k = 9 + -15k + -2k2

Solving
3 + -4k = 9 + -15k + -2k2

Solving for variable 'k'.

Reorder the terms:
3 + -9 + -4k + 15k + 2k2 = 9 + -15k + -2k2 + -9 + 15k + 2k2

Combine like terms: 3 + -9 = -6
-6 + -4k + 15k + 2k2 = 9 + -15k + -2k2 + -9 + 15k + 2k2

Combine like terms: -4k + 15k = 11k
-6 + 11k + 2k2 = 9 + -15k + -2k2 + -9 + 15k + 2k2

Reorder the terms:
-6 + 11k + 2k2 = 9 + -9 + -15k + 15k + -2k2 + 2k2

Combine like terms: 9 + -9 = 0
-6 + 11k + 2k2 = 0 + -15k + 15k + -2k2 + 2k2
-6 + 11k + 2k2 = -15k + 15k + -2k2 + 2k2

Combine like terms: -15k + 15k = 0
-6 + 11k + 2k2 = 0 + -2k2 + 2k2
-6 + 11k + 2k2 = -2k2 + 2k2

Combine like terms: -2k2 + 2k2 = 0
-6 + 11k + 2k2 = 0

Factor a trinomial.
(-6 + -1k)(1 + -2k) = 0


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 '(1 + -2k)' equal to zero and attempt to solve:

Simplifying
1 + -2k = 0

Solving
1 + -2k = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2k = 0 + -1
-2k = 0 + -1

Combine like terms: 0 + -1 = -1
-2k = -1

Divide each side by '-2'.
k = 0.5

Simplifying
k = 0.5
Solution
k = {-6, 0.5}

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