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

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


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

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

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

Solving
-2 + bx + 2k + 3kx + kx2 + x2 = 0

Solving for variable 'b'.

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

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

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

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

Combine like terms: 0 + 2 = 2
bx + 2k + 3kx + kx2 + x2 = 2

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

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

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

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

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

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

Add '-1kx2' to each side of the equation.
bx + kx2 + -1kx2 + x2 = 2 + -2k + -3kx + -1kx2

Combine like terms: kx2 + -1kx2 = 0
bx + 0 + x2 = 2 + -2k + -3kx + -1kx2
bx + x2 = 2 + -2k + -3kx + -1kx2

Add '-1x2' to each side of the equation.
bx + x2 + -1x2 = 2 + -2k + -3kx + -1kx2 + -1x2

Combine like terms: x2 + -1x2 = 0
bx + 0 = 2 + -2k + -3kx + -1kx2 + -1x2
bx = 2 + -2k + -3kx + -1kx2 + -1x2

Divide each side by 'x'.
b = 2x-1 + -2kx-1 + -3k + -1kx + -1x

Simplifying
b = 2x-1 + -2kx-1 + -3k + -1kx + -1x

Reorder the terms:
b = -3k + -2kx-1 + -1kx + 2x-1 + -1x

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