x^2+x+4=8x-2

Solution for x^2+x+4=8x-2 equation:

Simplifying
x2 + x + 4 = 8x + -2

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

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

Solving
4 + x + x2 = -2 + 8x

Solving for variable 'x'.

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

Combine like terms: 4 + 2 = 6
6 + x + -8x + x2 = -2 + 8x + 2 + -8x

Combine like terms: x + -8x = -7x
6 + -7x + x2 = -2 + 8x + 2 + -8x

Reorder the terms:
6 + -7x + x2 = -2 + 2 + 8x + -8x

Combine like terms: -2 + 2 = 0
6 + -7x + x2 = 0 + 8x + -8x
6 + -7x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
6 + -7x + x2 = 0

Factor a trinomial.
(1 + -1x)(6 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {1, 6}