5x^2-4x+2+k(4x^2-2x-1)=0

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Solution for 5x^2-4x+2+k(4x^2-2x-1)=0 equation: 


Simplifying
5x2 + -4x + 2 + k(4x2 + -2x + -1) = 0

Reorder the terms:
5x2 + -4x + 2 + k(-1 + -2x + 4x2) = 0
5x2 + -4x + 2 + (-1 * k + -2x * k + 4x2 * k) = 0
5x2 + -4x + 2 + (-1k + -2kx + 4kx2) = 0

Reorder the terms:
2 + -1k + -2kx + 4kx2 + -4x + 5x2 = 0

Solving
2 + -1k + -2kx + 4kx2 + -4x + 5x2 = 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 + -1k + -2kx + 4kx2 + -4x + -2 + 5x2 = 0 + -2

Reorder the terms:
2 + -2 + -1k + -2kx + 4kx2 + -4x + 5x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k + -2kx + 4kx2 + -4x + 5x2 = 0 + -2
-1k + -2kx + 4kx2 + -4x + 5x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1k + -2kx + 4kx2 + -4x + 5x2 = -2

Add '4x' to each side of the equation.
-1k + -2kx + 4kx2 + -4x + 4x + 5x2 = -2 + 4x

Combine like terms: -4x + 4x = 0
-1k + -2kx + 4kx2 + 0 + 5x2 = -2 + 4x
-1k + -2kx + 4kx2 + 5x2 = -2 + 4x

Add '-5x2' to each side of the equation.
-1k + -2kx + 4kx2 + 5x2 + -5x2 = -2 + 4x + -5x2

Combine like terms: 5x2 + -5x2 = 0
-1k + -2kx + 4kx2 + 0 = -2 + 4x + -5x2
-1k + -2kx + 4kx2 = -2 + 4x + -5x2

Reorder the terms:
2 + -1k + -2kx + 4kx2 + -4x + 5x2 = -2 + 4x + -5x2 + 2 + -4x + 5x2

Reorder the terms:
2 + -1k + -2kx + 4kx2 + -4x + 5x2 = -2 + 2 + 4x + -4x + -5x2 + 5x2

Combine like terms: -2 + 2 = 0
2 + -1k + -2kx + 4kx2 + -4x + 5x2 = 0 + 4x + -4x + -5x2 + 5x2
2 + -1k + -2kx + 4kx2 + -4x + 5x2 = 4x + -4x + -5x2 + 5x2

Combine like terms: 4x + -4x = 0
2 + -1k + -2kx + 4kx2 + -4x + 5x2 = 0 + -5x2 + 5x2
2 + -1k + -2kx + 4kx2 + -4x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
2 + -1k + -2kx + 4kx2 + -4x + 5x2 = 0

The solution to this equation could not be determined.

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