(3x+k)(9x^2+21x+k^2)=27x^3+k^3

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Solution for (3x+k)(9x^2+21x+k^2)=27x^3+k^3 equation: 


Simplifying
(3x + k)(9x2 + 21x + k2) = 27x3 + k3

Reorder the terms:
(k + 3x)(9x2 + 21x + k2) = 27x3 + k3

Reorder the terms:
(k + 3x)(k2 + 21x + 9x2) = 27x3 + k3

Multiply (k + 3x) * (k2 + 21x + 9x2)
(k(k2 + 21x + 9x2) + 3x * (k2 + 21x + 9x2)) = 27x3 + k3
((k2 * k + 21x * k + 9x2 * k) + 3x * (k2 + 21x + 9x2)) = 27x3 + k3

Reorder the terms:
((21kx + 9kx2 + k3) + 3x * (k2 + 21x + 9x2)) = 27x3 + k3
((21kx + 9kx2 + k3) + 3x * (k2 + 21x + 9x2)) = 27x3 + k3
(21kx + 9kx2 + k3 + (k2 * 3x + 21x * 3x + 9x2 * 3x)) = 27x3 + k3
(21kx + 9kx2 + k3 + (3k2x + 63x2 + 27x3)) = 27x3 + k3

Reorder the terms:
(21kx + 9kx2 + 3k2x + k3 + 63x2 + 27x3) = 27x3 + k3
(21kx + 9kx2 + 3k2x + k3 + 63x2 + 27x3) = 27x3 + k3

Reorder the terms:
21kx + 9kx2 + 3k2x + k3 + 63x2 + 27x3 = k3 + 27x3

Add '-1k3' to each side of the equation.
21kx + 9kx2 + 3k2x + k3 + 63x2 + -1k3 + 27x3 = k3 + -1k3 + 27x3

Reorder the terms:
21kx + 9kx2 + 3k2x + k3 + -1k3 + 63x2 + 27x3 = k3 + -1k3 + 27x3

Combine like terms: k3 + -1k3 = 0
21kx + 9kx2 + 3k2x + 0 + 63x2 + 27x3 = k3 + -1k3 + 27x3
21kx + 9kx2 + 3k2x + 63x2 + 27x3 = k3 + -1k3 + 27x3

Combine like terms: k3 + -1k3 = 0
21kx + 9kx2 + 3k2x + 63x2 + 27x3 = 0 + 27x3
21kx + 9kx2 + 3k2x + 63x2 + 27x3 = 27x3

Add '-27x3' to each side of the equation.
21kx + 9kx2 + 3k2x + 63x2 + 27x3 + -27x3 = 27x3 + -27x3

Combine like terms: 27x3 + -27x3 = 0
21kx + 9kx2 + 3k2x + 63x2 + 0 = 27x3 + -27x3
21kx + 9kx2 + 3k2x + 63x2 = 27x3 + -27x3

Combine like terms: 27x3 + -27x3 = 0
21kx + 9kx2 + 3k2x + 63x2 = 0

Solving
21kx + 9kx2 + 3k2x + 63x2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(7k + 3kx + k2 + 21x) = 0

Ignore the factor 3.

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

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(7k + 3kx + k2 + 21x)' equal to zero and attempt to solve:

Simplifying
7k + 3kx + k2 + 21x = 0

Solving
7k + 3kx + k2 + 21x = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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