0=x^2+13x-510

Solution for 0=x^2+13x-510 equation:

Simplifying
0 = x2 + 13x + -510

Reorder the terms:
0 = -510 + 13x + x2

Solving
0 = -510 + 13x + x2

Solving for variable 'x'.

Combine like terms: 0 + 510 = 510
510 + -13x + -1x2 = -510 + 13x + x2 + 510 + -13x + -1x2

Reorder the terms:
510 + -13x + -1x2 = -510 + 510 + 13x + -13x + x2 + -1x2

Combine like terms: -510 + 510 = 0
510 + -13x + -1x2 = 0 + 13x + -13x + x2 + -1x2
510 + -13x + -1x2 = 13x + -13x + x2 + -1x2

Combine like terms: 13x + -13x = 0
510 + -13x + -1x2 = 0 + x2 + -1x2
510 + -13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
510 + -13x + -1x2 = 0

Factor a trinomial.
(17 + -1x)(30 + x) = 0

Subproblem 1
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Subproblem 2
Set the factor '(30 + x)' equal to zero and attempt to solve:

Simplifying
30 + x = 0

Solving
30 + x = 0

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

Add '-30' to each side of the equation.
30 + -30 + x = 0 + -30

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

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

Simplifying
x = -30
Solution
x = {17, -30}