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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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