0=2x^2-x-6

Solution for 0=2x^2-x-6 equation:

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

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

Solving
0 = -6 + -1x + 2x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(2 + -1x)(3 + 2x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {2, -1.5}