0=2x^2-x-3

Solution for 0=2x^2-x-3 equation:

Simplifying
0 = 2x2 + -1x + -3

Reorder the terms:
0 = -3 + -1x + 2x2

Solving
0 = -3 + -1x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 3 = 3
3 + x + -2x2 = -3 + -1x + 2x2 + 3 + x + -2x2

Reorder the terms:
3 + x + -2x2 = -3 + 3 + -1x + x + 2x2 + -2x2

Combine like terms: -3 + 3 = 0
3 + x + -2x2 = 0 + -1x + x + 2x2 + -2x2
3 + x + -2x2 = -1x + x + 2x2 + -2x2

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

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

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

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {1.5, -1}