4x^2+x+6=8x+3

Solution for 4x^2+x+6=8x+3 equation:

Simplifying
4x2 + x + 6 = 8x + 3

Reorder the terms:
6 + x + 4x2 = 8x + 3

Reorder the terms:
6 + x + 4x2 = 3 + 8x

Solving
6 + x + 4x2 = 3 + 8x

Solving for variable 'x'.

Reorder the terms:
6 + -3 + x + -8x + 4x2 = 3 + 8x + -3 + -8x

Combine like terms: 6 + -3 = 3
3 + x + -8x + 4x2 = 3 + 8x + -3 + -8x

Combine like terms: x + -8x = -7x
3 + -7x + 4x2 = 3 + 8x + -3 + -8x

Reorder the terms:
3 + -7x + 4x2 = 3 + -3 + 8x + -8x

Combine like terms: 3 + -3 = 0
3 + -7x + 4x2 = 0 + 8x + -8x
3 + -7x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
3 + -7x + 4x2 = 0

Factor a trinomial.
(3 + -4x)(1 + -1x) = 0

Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

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

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
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 = {0.75, 1}