6x^2+3x-2k(x^2+x+1)-2=0

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Solution for 6x^2+3x-2k(x^2+x+1)-2=0 equation: 


Simplifying
6x2 + 3x + -2k(x2 + x + 1) + -2 = 0

Reorder the terms:
6x2 + 3x + -2k(1 + x + x2) + -2 = 0
6x2 + 3x + (1 * -2k + x * -2k + x2 * -2k) + -2 = 0
6x2 + 3x + (-2k + -2kx + -2kx2) + -2 = 0

Reorder the terms:
-2 + -2k + -2kx + -2kx2 + 3x + 6x2 = 0

Solving
-2 + -2k + -2kx + -2kx2 + 3x + 6x2 = 0

Solving for variable 'k'.

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

Add '2' to each side of the equation.
-2 + -2k + -2kx + -2kx2 + 3x + 2 + 6x2 = 0 + 2

Reorder the terms:
-2 + 2 + -2k + -2kx + -2kx2 + 3x + 6x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -2k + -2kx + -2kx2 + 3x + 6x2 = 0 + 2
-2k + -2kx + -2kx2 + 3x + 6x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-2k + -2kx + -2kx2 + 3x + 6x2 = 2

Add '-3x' to each side of the equation.
-2k + -2kx + -2kx2 + 3x + -3x + 6x2 = 2 + -3x

Combine like terms: 3x + -3x = 0
-2k + -2kx + -2kx2 + 0 + 6x2 = 2 + -3x
-2k + -2kx + -2kx2 + 6x2 = 2 + -3x

Add '-6x2' to each side of the equation.
-2k + -2kx + -2kx2 + 6x2 + -6x2 = 2 + -3x + -6x2

Combine like terms: 6x2 + -6x2 = 0
-2k + -2kx + -2kx2 + 0 = 2 + -3x + -6x2
-2k + -2kx + -2kx2 = 2 + -3x + -6x2

Reorder the terms:
-2 + -2k + -2kx + -2kx2 + 3x + 6x2 = 2 + -3x + -6x2 + -2 + 3x + 6x2

Reorder the terms:
-2 + -2k + -2kx + -2kx2 + 3x + 6x2 = 2 + -2 + -3x + 3x + -6x2 + 6x2

Combine like terms: 2 + -2 = 0
-2 + -2k + -2kx + -2kx2 + 3x + 6x2 = 0 + -3x + 3x + -6x2 + 6x2
-2 + -2k + -2kx + -2kx2 + 3x + 6x2 = -3x + 3x + -6x2 + 6x2

Combine like terms: -3x + 3x = 0
-2 + -2k + -2kx + -2kx2 + 3x + 6x2 = 0 + -6x2 + 6x2
-2 + -2k + -2kx + -2kx2 + 3x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-2 + -2k + -2kx + -2kx2 + 3x + 6x2 = 0

The solution to this equation could not be determined.

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