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

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


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

Reorder the terms:
2x2 + (-3kx + 3x) = 0
2x2 + (-3kx + 3x) = 0

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

Solving
-3kx + 3x + 2x2 = 0

Solving for variable 'k'.

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

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

Combine like terms: 3x + -3x = 0
-3kx + 0 + 2x2 = 0 + -3x
-3kx + 2x2 = 0 + -3x
Remove the zero:
-3kx + 2x2 = -3x

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

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

Divide each side by '-3x'.
k = 1 + 0.6666666667x

Simplifying
k = 1 + 0.6666666667x

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