0=2x^2-x-21

Solution for 0=2x^2-x-21 equation:

Simplifying
0 = 2x2 + -1x + -21

Reorder the terms:
0 = -21 + -1x + 2x2

Solving
0 = -21 + -1x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 21 = 21
21 + x + -2x2 = -21 + -1x + 2x2 + 21 + x + -2x2

Reorder the terms:
21 + x + -2x2 = -21 + 21 + -1x + x + 2x2 + -2x2

Combine like terms: -21 + 21 = 0
21 + x + -2x2 = 0 + -1x + x + 2x2 + -2x2
21 + x + -2x2 = -1x + x + 2x2 + -2x2

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

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

Factor a trinomial.
(7 + -2x)(3 + x) = 0

Subproblem 1
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {3.5, -3}