12(k-4)+(5(k+3)(k-4))=-24(k+3)

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Solution for 12(k-4)+(5(k+3)(k-4))=-24(k+3) equation: 


Simplifying
12(k + -4) + (5(k + 3)(k + -4)) = -24(k + 3)

Reorder the terms:
12(-4 + k) + (5(k + 3)(k + -4)) = -24(k + 3)
(-4 * 12 + k * 12) + (5(k + 3)(k + -4)) = -24(k + 3)
(-48 + 12k) + (5(k + 3)(k + -4)) = -24(k + 3)

Reorder the terms:
-48 + 12k + (5(3 + k)(k + -4)) = -24(k + 3)

Reorder the terms:
-48 + 12k + (5(3 + k)(-4 + k)) = -24(k + 3)

Multiply (3 + k) * (-4 + k)
-48 + 12k + (5(3(-4 + k) + k(-4 + k))) = -24(k + 3)
-48 + 12k + (5((-4 * 3 + k * 3) + k(-4 + k))) = -24(k + 3)
-48 + 12k + (5((-12 + 3k) + k(-4 + k))) = -24(k + 3)
-48 + 12k + (5(-12 + 3k + (-4 * k + k * k))) = -24(k + 3)
-48 + 12k + (5(-12 + 3k + (-4k + k2))) = -24(k + 3)

Combine like terms: 3k + -4k = -1k
-48 + 12k + (5(-12 + -1k + k2)) = -24(k + 3)
-48 + 12k + ((-12 * 5 + -1k * 5 + k2 * 5)) = -24(k + 3)
-48 + 12k + ((-60 + -5k + 5k2)) = -24(k + 3)
-48 + 12k + (-60 + -5k + 5k2) = -24(k + 3)

Remove parenthesis around (-60 + -5k + 5k2)
-48 + 12k + -60 + -5k + 5k2 = -24(k + 3)

Reorder the terms:
-48 + -60 + 12k + -5k + 5k2 = -24(k + 3)

Combine like terms: -48 + -60 = -108
-108 + 12k + -5k + 5k2 = -24(k + 3)

Combine like terms: 12k + -5k = 7k
-108 + 7k + 5k2 = -24(k + 3)

Reorder the terms:
-108 + 7k + 5k2 = -24(3 + k)
-108 + 7k + 5k2 = (3 * -24 + k * -24)
-108 + 7k + 5k2 = (-72 + -24k)

Solving
-108 + 7k + 5k2 = -72 + -24k

Solving for variable 'k'.

Reorder the terms:
-108 + 72 + 7k + 24k + 5k2 = -72 + -24k + 72 + 24k

Combine like terms: -108 + 72 = -36
-36 + 7k + 24k + 5k2 = -72 + -24k + 72 + 24k

Combine like terms: 7k + 24k = 31k
-36 + 31k + 5k2 = -72 + -24k + 72 + 24k

Reorder the terms:
-36 + 31k + 5k2 = -72 + 72 + -24k + 24k

Combine like terms: -72 + 72 = 0
-36 + 31k + 5k2 = 0 + -24k + 24k
-36 + 31k + 5k2 = -24k + 24k

Combine like terms: -24k + 24k = 0
-36 + 31k + 5k2 = 0

Factor a trinomial.
(-36 + -5k)(1 + -1k) = 0


Subproblem 1
Set the factor '(-36 + -5k)' equal to zero and attempt to solve:

Simplifying
-36 + -5k = 0

Solving
-36 + -5k = 0

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

Add '36' to each side of the equation.
-36 + 36 + -5k = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -5k = 0 + 36
-5k = 0 + 36

Combine like terms: 0 + 36 = 36
-5k = 36

Divide each side by '-5'.
k = -7.2

Simplifying
k = -7.2

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

Simplifying
1 + -1k = 0

Solving
1 + -1k = 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 + -1k = 0 + -1

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

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

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

Simplifying
k = 1
Solution
k = {-7.2, 1}

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