kx^2+3kx+k=0

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Solution for kx^2+3kx+k=0 equation: 


Simplifying
kx2 + 3kx + k = 0

Reorder the terms:
k + 3kx + kx2 = 0

Solving
k + 3kx + kx2 = 0

Solving for variable 'k'.

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

Factor out the Greatest Common Factor (GCF), 'k'.
k(1 + 3x + x2) = 0


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 '(1 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
1 + 3x + x2 = 0

Solving
1 + 3x + x2 = 0

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

Add '-1' to each side of the equation.
1 + 3x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 3x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x + x2 = 0 + -1
3x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
3x + x2 = -1

Add '-3x' to each side of the equation.
3x + -3x + x2 = -1 + -3x

Combine like terms: 3x + -3x = 0
0 + x2 = -1 + -3x
x2 = -1 + -3x

Add '-1x2' to each side of the equation.
x2 + -1x2 = -1 + -3x + -1x2

Combine like terms: x2 + -1x2 = 0
0 = -1 + -3x + -1x2

Simplifying
0 = -1 + -3x + -1x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
k = {0}

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