x^2-(3k+2)x+2(2k+1)=x^2+(3k+8)x-2(2k-1)

Solution for x^2-(3k+2)x+2(2k+1)=x^2+(3k+8)x-2(2k-1) equation:

Simplifying
x2 + -1(3k + 2) * x + 2(2k + 1) = x2 + (3k + 8) * x + -2(2k + -1)

Reorder the terms:
x2 + -1(2 + 3k) * x + 2(2k + 1) = x2 + (3k + 8) * x + -2(2k + -1)

Reorder the terms for easier multiplication:
x2 + -1x(2 + 3k) + 2(2k + 1) = x2 + (3k + 8) * x + -2(2k + -1)
x2 + (2 * -1x + 3k * -1x) + 2(2k + 1) = x2 + (3k + 8) * x + -2(2k + -1)

Reorder the terms:
x2 + (-3kx + -2x) + 2(2k + 1) = x2 + (3k + 8) * x + -2(2k + -1)
x2 + (-3kx + -2x) + 2(2k + 1) = x2 + (3k + 8) * x + -2(2k + -1)

Reorder the terms:
x2 + -3kx + -2x + 2(1 + 2k) = x2 + (3k + 8) * x + -2(2k + -1)
x2 + -3kx + -2x + (1 * 2 + 2k * 2) = x2 + (3k + 8) * x + -2(2k + -1)
x2 + -3kx + -2x + (2 + 4k) = x2 + (3k + 8) * x + -2(2k + -1)

Reorder the terms:
2 + 4k + -3kx + -2x + x2 = x2 + (3k + 8) * x + -2(2k + -1)

Reorder the terms:
2 + 4k + -3kx + -2x + x2 = x2 + (8 + 3k) * x + -2(2k + -1)

Reorder the terms for easier multiplication:
2 + 4k + -3kx + -2x + x2 = x2 + x(8 + 3k) + -2(2k + -1)
2 + 4k + -3kx + -2x + x2 = x2 + (8 * x + 3k * x) + -2(2k + -1)

Reorder the terms:
2 + 4k + -3kx + -2x + x2 = x2 + (3kx + 8x) + -2(2k + -1)
2 + 4k + -3kx + -2x + x2 = x2 + (3kx + 8x) + -2(2k + -1)

Reorder the terms:
2 + 4k + -3kx + -2x + x2 = x2 + 3kx + 8x + -2(-1 + 2k)
2 + 4k + -3kx + -2x + x2 = x2 + 3kx + 8x + (-1 * -2 + 2k * -2)
2 + 4k + -3kx + -2x + x2 = x2 + 3kx + 8x + (2 + -4k)

Reorder the terms:
2 + 4k + -3kx + -2x + x2 = 2 + -4k + 3kx + 8x + x2

Add '-2' to each side of the equation.
2 + 4k + -3kx + -2x + -2 + x2 = 2 + -4k + 3kx + 8x + -2 + x2

Reorder the terms:
2 + -2 + 4k + -3kx + -2x + x2 = 2 + -4k + 3kx + 8x + -2 + x2

Combine like terms: 2 + -2 = 0
0 + 4k + -3kx + -2x + x2 = 2 + -4k + 3kx + 8x + -2 + x2
4k + -3kx + -2x + x2 = 2 + -4k + 3kx + 8x + -2 + x2

Reorder the terms:
4k + -3kx + -2x + x2 = 2 + -2 + -4k + 3kx + 8x + x2

Combine like terms: 2 + -2 = 0
4k + -3kx + -2x + x2 = 0 + -4k + 3kx + 8x + x2
4k + -3kx + -2x + x2 = -4k + 3kx + 8x + x2

Add '-1x2' to each side of the equation.
4k + -3kx + -2x + x2 + -1x2 = -4k + 3kx + 8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4k + -3kx + -2x + 0 = -4k + 3kx + 8x + x2 + -1x2
4k + -3kx + -2x = -4k + 3kx + 8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4k + -3kx + -2x = -4k + 3kx + 8x + 0
4k + -3kx + -2x = -4k + 3kx + 8x

Solving
4k + -3kx + -2x = -4k + 3kx + 8x

Solving for variable 'k'.

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

Add '4k' to each side of the equation.
4k + -3kx + 4k + -2x = -4k + 3kx + 4k + 8x

Reorder the terms:
4k + 4k + -3kx + -2x = -4k + 3kx + 4k + 8x

Combine like terms: 4k + 4k = 8k
8k + -3kx + -2x = -4k + 3kx + 4k + 8x

Reorder the terms:
8k + -3kx + -2x = -4k + 4k + 3kx + 8x

Combine like terms: -4k + 4k = 0
8k + -3kx + -2x = 0 + 3kx + 8x
8k + -3kx + -2x = 3kx + 8x

Add '-3kx' to each side of the equation.
8k + -3kx + -3kx + -2x = 3kx + -3kx + 8x

Combine like terms: -3kx + -3kx = -6kx
8k + -6kx + -2x = 3kx + -3kx + 8x

Combine like terms: 3kx + -3kx = 0
8k + -6kx + -2x = 0 + 8x
8k + -6kx + -2x = 8x

Add '2x' to each side of the equation.
8k + -6kx + -2x + 2x = 8x + 2x

Combine like terms: -2x + 2x = 0
8k + -6kx + 0 = 8x + 2x
8k + -6kx = 8x + 2x

Combine like terms: 8x + 2x = 10x
8k + -6kx = 10x

Combine like terms: 10x + -10x = 0
8k + -6kx + -10x = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4k + -3kx + -5x) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4k + -3kx + -5x)' equal to zero and attempt to solve:

Simplifying
4k + -3kx + -5x = 0

Solving
4k + -3kx + -5x = 0

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

Add '5x' to each side of the equation.
4k + -3kx + -5x + 5x = 0 + 5x

Combine like terms: -5x + 5x = 0
4k + -3kx + 0 = 0 + 5x
4k + -3kx = 0 + 5x
Remove the zero:
4k + -3kx = 5x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.