0=x^2-x-30

Solution for 0=x^2-x-30 equation:

Simplifying
0 = x2 + -1x + -30

Reorder the terms:
0 = -30 + -1x + x2

Solving
0 = -30 + -1x + x2

Solving for variable 'x'.

Combine like terms: 0 + 30 = 30
30 + x + -1x2 = -30 + -1x + x2 + 30 + x + -1x2

Reorder the terms:
30 + x + -1x2 = -30 + 30 + -1x + x + x2 + -1x2

Combine like terms: -30 + 30 = 0
30 + x + -1x2 = 0 + -1x + x + x2 + -1x2
30 + x + -1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
30 + x + -1x2 = 0 + x2 + -1x2
30 + x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
30 + x + -1x2 = 0

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

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5
Solution
x = {6, -5}