(x-2)4+6x=x(x+1)

Solution for (x-2)4+6x=x(x+1) equation:

Simplifying
(x + -2) * 4 + 6x = x(x + 1)

Reorder the terms:
(-2 + x) * 4 + 6x = x(x + 1)

Reorder the terms for easier multiplication:
4(-2 + x) + 6x = x(x + 1)
(-2 * 4 + x * 4) + 6x = x(x + 1)
(-8 + 4x) + 6x = x(x + 1)

Combine like terms: 4x + 6x = 10x
-8 + 10x = x(x + 1)

Reorder the terms:
-8 + 10x = x(1 + x)
-8 + 10x = (1 * x + x * x)
-8 + 10x = (1x + x2)

Solving
-8 + 10x = 1x + x2

Solving for variable 'x'.

Combine like terms: 10x + -1x = 9x
-8 + 9x + -1x2 = 1x + x2 + -1x + -1x2

Reorder the terms:
-8 + 9x + -1x2 = 1x + -1x + x2 + -1x2

Combine like terms: 1x + -1x = 0
-8 + 9x + -1x2 = 0 + x2 + -1x2
-8 + 9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8 + 9x + -1x2 = 0

Factor a trinomial.
(-8 + x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {8, 1}