6x^2+2x=5+x

Solution for 6x^2+2x=5+x equation:

Simplifying
6x2 + 2x = 5 + x

Reorder the terms:
2x + 6x2 = 5 + x

Solving
2x + 6x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
-5 + 2x + -1x + 6x2 = 5 + x + -5 + -1x

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

Reorder the terms:
-5 + 1x + 6x2 = 5 + -5 + x + -1x

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

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

Factor a trinomial.
(-1 + -1x)(5 + -6x) = 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 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333
Solution
x = {-1, 0.8333333333}