2x^2+13x=2x+6

Solution for 2x^2+13x=2x+6 equation:

Simplifying
2x2 + 13x = 2x + 6

Reorder the terms:
13x + 2x2 = 2x + 6

Reorder the terms:
13x + 2x2 = 6 + 2x

Solving
13x + 2x2 = 6 + 2x

Solving for variable 'x'.

Reorder the terms:
-6 + 13x + -2x + 2x2 = 6 + 2x + -6 + -2x

Combine like terms: 13x + -2x = 11x
-6 + 11x + 2x2 = 6 + 2x + -6 + -2x

Reorder the terms:
-6 + 11x + 2x2 = 6 + -6 + 2x + -2x

Combine like terms: 6 + -6 = 0
-6 + 11x + 2x2 = 0 + 2x + -2x
-6 + 11x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-6 + 11x + 2x2 = 0

Factor a trinomial.
(-6 + -1x)(1 + -2x) = 0

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-6, 0.5}