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

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

Simplifying
6x2 + x + 1 + -1x(2x + 6) = 0

Reorder the terms:
6x2 + x + 1 + -1x(6 + 2x) = 0
6x2 + x + 1 + (6 * -1x + 2x * -1x) = 0
6x2 + x + 1 + (-6x + -2x2) = 0

Reorder the terms:
1 + x + -6x + 6x2 + -2x2 = 0

Combine like terms: x + -6x = -5x
1 + -5x + 6x2 + -2x2 = 0

Combine like terms: 6x2 + -2x2 = 4x2
1 + -5x + 4x2 = 0

Solving
1 + -5x + 4x2 = 0

Solving for variable 'x'.

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

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

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
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 = {0.25, 1}