3k(2k+8)(3k-9)=0

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Solution for 3k(2k+8)(3k-9)=0 equation: 


Simplifying
3k(2k + 8)(3k + -9) = 0

Reorder the terms:
3k(8 + 2k)(3k + -9) = 0

Reorder the terms:
3k(8 + 2k)(-9 + 3k) = 0

Multiply (8 + 2k) * (-9 + 3k)
3k(8(-9 + 3k) + 2k * (-9 + 3k)) = 0
3k((-9 * 8 + 3k * 8) + 2k * (-9 + 3k)) = 0
3k((-72 + 24k) + 2k * (-9 + 3k)) = 0
3k(-72 + 24k + (-9 * 2k + 3k * 2k)) = 0
3k(-72 + 24k + (-18k + 6k2)) = 0

Combine like terms: 24k + -18k = 6k
3k(-72 + 6k + 6k2) = 0
(-72 * 3k + 6k * 3k + 6k2 * 3k) = 0
(-216k + 18k2 + 18k3) = 0

Solving
-216k + 18k2 + 18k3 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '18k'.
18k(-12 + k + k2) = 0

Factor a trinomial.
18k((-4 + -1k)(3 + -1k)) = 0

Ignore the factor 18.

Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0

Subproblem 2
Set the factor '(-4 + -1k)' equal to zero and attempt to solve:

Simplifying
-4 + -1k = 0

Solving
-4 + -1k = 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 + -1k = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1k = 0 + 4
-1k = 0 + 4

Combine like terms: 0 + 4 = 4
-1k = 4

Divide each side by '-1'.
k = -4

Simplifying
k = -4

Subproblem 3
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1k = 0 + -3
-1k = 0 + -3

Combine like terms: 0 + -3 = -3
-1k = -3

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Solution
k = {0, -4, 3}

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