6k(k+4)+3=5(k^2-12)+8k

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Solution for 6k(k+4)+3=5(k^2-12)+8k equation: 


Simplifying
6k(k + 4) + 3 = 5(k2 + -12) + 8k

Reorder the terms:
6k(4 + k) + 3 = 5(k2 + -12) + 8k
(4 * 6k + k * 6k) + 3 = 5(k2 + -12) + 8k
(24k + 6k2) + 3 = 5(k2 + -12) + 8k

Reorder the terms:
3 + 24k + 6k2 = 5(k2 + -12) + 8k

Reorder the terms:
3 + 24k + 6k2 = 5(-12 + k2) + 8k
3 + 24k + 6k2 = (-12 * 5 + k2 * 5) + 8k
3 + 24k + 6k2 = (-60 + 5k2) + 8k

Reorder the terms:
3 + 24k + 6k2 = -60 + 8k + 5k2

Solving
3 + 24k + 6k2 = -60 + 8k + 5k2

Solving for variable 'k'.

Reorder the terms:
3 + 60 + 24k + -8k + 6k2 + -5k2 = -60 + 8k + 5k2 + 60 + -8k + -5k2

Combine like terms: 3 + 60 = 63
63 + 24k + -8k + 6k2 + -5k2 = -60 + 8k + 5k2 + 60 + -8k + -5k2

Combine like terms: 24k + -8k = 16k
63 + 16k + 6k2 + -5k2 = -60 + 8k + 5k2 + 60 + -8k + -5k2

Combine like terms: 6k2 + -5k2 = 1k2
63 + 16k + 1k2 = -60 + 8k + 5k2 + 60 + -8k + -5k2

Reorder the terms:
63 + 16k + 1k2 = -60 + 60 + 8k + -8k + 5k2 + -5k2

Combine like terms: -60 + 60 = 0
63 + 16k + 1k2 = 0 + 8k + -8k + 5k2 + -5k2
63 + 16k + 1k2 = 8k + -8k + 5k2 + -5k2

Combine like terms: 8k + -8k = 0
63 + 16k + 1k2 = 0 + 5k2 + -5k2
63 + 16k + 1k2 = 5k2 + -5k2

Combine like terms: 5k2 + -5k2 = 0
63 + 16k + 1k2 = 0

Factor a trinomial.
(9 + k)(7 + k) = 0


Subproblem 1
Set the factor '(9 + k)' equal to zero and attempt to solve:

Simplifying
9 + k = 0

Solving
9 + k = 0

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

Add '-9' to each side of the equation.
9 + -9 + k = 0 + -9

Combine like terms: 9 + -9 = 0
0 + k = 0 + -9
k = 0 + -9

Combine like terms: 0 + -9 = -9
k = -9

Simplifying
k = -9

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

Simplifying
7 + k = 0

Solving
7 + k = 0

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

Add '-7' to each side of the equation.
7 + -7 + k = 0 + -7

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

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

Simplifying
k = -7
Solution
k = {-9, -7}

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