4x^2-x+6=8x+1

Solution for 4x^2-x+6=8x+1 equation:

Simplifying
4x2 + -1x + 6 = 8x + 1

Reorder the terms:
6 + -1x + 4x2 = 8x + 1

Reorder the terms:
6 + -1x + 4x2 = 1 + 8x

Solving
6 + -1x + 4x2 = 1 + 8x

Solving for variable 'x'.

Reorder the terms:
6 + -1 + -1x + -8x + 4x2 = 1 + 8x + -1 + -8x

Combine like terms: 6 + -1 = 5
5 + -1x + -8x + 4x2 = 1 + 8x + -1 + -8x

Combine like terms: -1x + -8x = -9x
5 + -9x + 4x2 = 1 + 8x + -1 + -8x

Reorder the terms:
5 + -9x + 4x2 = 1 + -1 + 8x + -8x

Combine like terms: 1 + -1 = 0
5 + -9x + 4x2 = 0 + 8x + -8x
5 + -9x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
5 + -9x + 4x2 = 0

Factor a trinomial.
(1 + -1x)(5 + -4x) = 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 '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 0

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

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

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {1, 1.25}