9x^2-6x+k^2=0

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Solution for 9x^2-6x+k^2=0 equation: 


Simplifying
9x2 + -6x + k2 = 0

Reorder the terms:
k2 + -6x + 9x2 = 0

Solving
k2 + -6x + 9x2 = 0

Solving for variable 'k'.

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

Add '6x' to each side of the equation.
k2 + -6x + 6x + 9x2 = 0 + 6x

Combine like terms: -6x + 6x = 0
k2 + 0 + 9x2 = 0 + 6x
k2 + 9x2 = 0 + 6x
Remove the zero:
k2 + 9x2 = 6x

Add '-9x2' to each side of the equation.
k2 + 9x2 + -9x2 = 6x + -9x2

Combine like terms: 9x2 + -9x2 = 0
k2 + 0 = 6x + -9x2
k2 = 6x + -9x2

Simplifying
k2 = 6x + -9x2

Reorder the terms:
k2 + -6x + 9x2 = 6x + -6x + -9x2 + 9x2

Combine like terms: 6x + -6x = 0
k2 + -6x + 9x2 = 0 + -9x2 + 9x2
k2 + -6x + 9x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
k2 + -6x + 9x2 = 0

Factor a trinomial.
(k + -3x)(k + -3x) = 0


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

Simplifying
k + -3x = 0

Solving
k + -3x = 0

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

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

Combine like terms: -3x + 3x = 0
k + 0 = 0 + 3x
k = 0 + 3x
Remove the zero:
k = 3x

Simplifying
k = 3x

Subproblem 2
Set the factor '(k + -3x)' equal to zero and attempt to solve:

Simplifying
k + -3x = 0

Solving
k + -3x = 0

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

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

Combine like terms: -3x + 3x = 0
k + 0 = 0 + 3x
k = 0 + 3x
Remove the zero:
k = 3x

Simplifying
k = 3x
Solution
k = {3x, 3x}

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