9x^2-2(3x+1)x-1+k^2=0

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Solution for 9x^2-2(3x+1)x-1+k^2=0 equation: 


Simplifying
9x2 + -2(3x + 1) * x + -1 + k2 = 0

Reorder the terms:
9x2 + -2(1 + 3x) * x + -1 + k2 = 0

Reorder the terms for easier multiplication:
9x2 + -2x(1 + 3x) + -1 + k2 = 0
9x2 + (1 * -2x + 3x * -2x) + -1 + k2 = 0
9x2 + (-2x + -6x2) + -1 + k2 = 0

Reorder the terms:
-1 + k2 + -2x + 9x2 + -6x2 = 0

Combine like terms: 9x2 + -6x2 = 3x2
-1 + k2 + -2x + 3x2 = 0

Solving
-1 + k2 + -2x + 3x2 = 0

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + k2 + -2x + 1 + 3x2 = 0 + 1

Reorder the terms:
-1 + 1 + k2 + -2x + 3x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + k2 + -2x + 3x2 = 0 + 1
k2 + -2x + 3x2 = 0 + 1

Combine like terms: 0 + 1 = 1
k2 + -2x + 3x2 = 1

Add '2x' to each side of the equation.
k2 + -2x + 2x + 3x2 = 1 + 2x

Combine like terms: -2x + 2x = 0
k2 + 0 + 3x2 = 1 + 2x
k2 + 3x2 = 1 + 2x

Add '-3x2' to each side of the equation.
k2 + 3x2 + -3x2 = 1 + 2x + -3x2

Combine like terms: 3x2 + -3x2 = 0
k2 + 0 = 1 + 2x + -3x2
k2 = 1 + 2x + -3x2

Simplifying
k2 = 1 + 2x + -3x2

Reorder the terms:
-1 + k2 + -2x + 3x2 = 1 + 2x + -3x2 + -1 + -2x + 3x2

Reorder the terms:
-1 + k2 + -2x + 3x2 = 1 + -1 + 2x + -2x + -3x2 + 3x2

Combine like terms: 1 + -1 = 0
-1 + k2 + -2x + 3x2 = 0 + 2x + -2x + -3x2 + 3x2
-1 + k2 + -2x + 3x2 = 2x + -2x + -3x2 + 3x2

Combine like terms: 2x + -2x = 0
-1 + k2 + -2x + 3x2 = 0 + -3x2 + 3x2
-1 + k2 + -2x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-1 + k2 + -2x + 3x2 = 0

The solution to this equation could not be determined.

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