0=2(x^2+8x-513)

Solution for 0=2(x^2+8x-513) equation:

Simplifying
0 = 2(x2 + 8x + -513)

Reorder the terms:
0 = 2(-513 + 8x + x2)
0 = (-513 * 2 + 8x * 2 + x2 * 2)
0 = (-1026 + 16x + 2x2)

Solving
0 = -1026 + 16x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 1026 = 1026
1026 + -16x + -2x2 = -1026 + 16x + 2x2 + 1026 + -16x + -2x2

Reorder the terms:
1026 + -16x + -2x2 = -1026 + 1026 + 16x + -16x + 2x2 + -2x2

Combine like terms: -1026 + 1026 = 0
1026 + -16x + -2x2 = 0 + 16x + -16x + 2x2 + -2x2
1026 + -16x + -2x2 = 16x + -16x + 2x2 + -2x2

Combine like terms: 16x + -16x = 0
1026 + -16x + -2x2 = 0 + 2x2 + -2x2
1026 + -16x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1026 + -16x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(513 + -8x + -1x2) = 0

Factor a trinomial.
2((19 + -1x)(27 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(19 + -1x)' equal to zero and attempt to solve:

Simplifying
19 + -1x = 0

Solving
19 + -1x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1x = 0 + -19
-1x = 0 + -19

Combine like terms: 0 + -19 = -19
-1x = -19

Divide each side by '-1'.
x = 19

Simplifying
x = 19
Subproblem 2
Set the factor '(27 + x)' equal to zero and attempt to solve:

Simplifying
27 + x = 0

Solving
27 + x = 0

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

Add '-27' to each side of the equation.
27 + -27 + x = 0 + -27

Combine like terms: 27 + -27 = 0
0 + x = 0 + -27
x = 0 + -27

Combine like terms: 0 + -27 = -27
x = -27

Simplifying
x = -27
Solution
x = {19, -27}